j 


XT, 


ot. 


ELEMENTARY    LESSONS 


IN 


ELECTRICITY  AND  MAGNETISM 


A  MAP  OF  ENGLAND. 

SHEWING  THE  LINES  OF  EQUAL  MAGNETIC  DECLINATION 
AND  THOSE  OF  EQUAL  DIP  &  INTENSITY. 

FOR  THE  YEAR.  1888 


ELEMENTARY  LESSONS  IN 

ELECTRICITT 

and  Magnetism 

By  SILVANUS   P.   THOMPSON,  D.Sc.,  B.A.,  F.R.A.S. 

PRINCIPAL  OF  AND  PROFESSOR  OF  PHYSICS  IN  THE  CITY  AND  GUILDS  OF  LONDON 
TECHNICAL  COLLEGE,  FINSBURY  j  LATE  PROFESSOR  OF  EXPERIMENTAL  PHYSICS  IN 
UNIVERSITY  COLLEGE,  BRISTOL  littSttlltitttti 


R.     F  .    FENNO    AND     COMPANY 

N  I  N  E  A  N  D  E  L  EVE  N  EAST  SIXTEENTH  STREET 

NEW   YORK    CITY 


PREFACE. 

These  Lessons  in  Electricity  and  Magnetism  are  in- 
tended to  afford  to  beginners  a  clear  and  accurate  knowl- 
edge of  the  experiments  upon  which  the  Sciences  of  Elec- 
tricity and  Magnetism  are  based,  and  of  the  exact  laws 
which  have  been  thereby  discovered.  The  difficulties 
which  beginners  find  in  studying  many  modern  text-books 
arise  partly  from  the  very  wide  range  of  the  subject,  and 
partly  from  want  of  familiarity  with  the  simple  fundamental 
experiments.  We  have,  at  the  outset,  three  distinct  sets 
of  phenomena  to  observe,  viz. — those  of  Frictional  Electri- 
city, of  Current  Electricity,  and  of  Magnetism  ;  and  yet  it 
is  impossible  to  study  any  one  of  these  rightly  without 
knowing  something  of  them  all.  Accordingly,  the  first 
three  chapters  of  this  work  are  devoted  to  a  simple  expo- 
sition of  the  prominent  experimental  facts  of  these  three 
branches  of  the  subject,  reserving  until  the  later  chapters 
the  points  of  connection  between  them,  and  such  parts  of 
electrical  theory  as  are  admissible  in  a  strictly  elementary 
work.  No  knowledge  of  algebra  beyond  simple  equations, 
or  of  geometry  beyond  the  first  book  of  Euclid,  is  assumed. 

A  series  of  Exercises  and  Problems  has  been  added  at 
the  end  of  the  book  in  order  that  students,  who  so  desire, 
may  test  their  power  of  applying  thought  to  what  they 
read,  and  of  ascertaining,  by  answering  the  questions  or 
working  the  problems,  how  far  they  have  digested  what 
they  have  read  and  made  it  their  own. 

Wherever  it  has  been  necessary  to  state  electrical 


2068176 


vi  PREFACE. 

quantities  numerically,  the  practical  system  of  electrical 
units  (employing  the  volt,  the  ohm,  and  the  ampere,  as  units 
of  electromotive-force,  resistance  and  current,  respectively) 
has  been  resorted  to  in  preference  to  any  other  system. 
The  author  has  adopted  this  course  purposely,  because  he 
has  found  by  experience  that  these  units  gradually  acquire, 
in  the  minds  of  students  of  electricity,  a  concreteness  and 
reality  not  possessed  by  any  mere  abstract  units,  and  be- 
cause it  is  hoped  that  the  lessons  will  be  thereby  rendered 
more  useful  to  young  telegraphists  to  whom  these  units  are 
already  familiar,  and  who  may  desire  to  learn  something 
of  the  Science  of  Electricity  beyond  the  narrow  limits  of 
their  own  practical  work. 

Students  should  remember  that  this  little  work  is  but 
the  introduction  to  a  very  widely-extended  science,  and 
those  who  desire  not  to  stop  short  at  the  first  step  should 
consult  the  larger  treatises  of  Faraday,  Maxwell,  Thom- 
son, Wiedemann,  and  Mascart,  as  well  as  the  more 
special  works  which  deal  with  the  various  technical 
Applications  of  the  Science  of  Electricity  to  the  Arts 
and  Manufactures.  Though  the  Author  does  not  think 
it  well  in  an  elementary  text-book  to  emphasize  particular 
theories  on  the  nature  of  Electricity  upon  which  the 
highest  authorities  are  not  yet  agreed,  he  believes  that 
it  will  add  to  a  clear  understanding  of  the  matter  if  he 
states  his  own  views  on  the  subject. 

The  theory  of  electricity  adopted  throughout  these 
Lessons  is,  that  Electricity,  whatever  its  true  nature,  is 
one,  not  two:  that  this  Electricity,  whatever  it  may 
prove  to  be,  is  not  matter,  and  is  not  energy ;  that  it 


PREFACE.  vll 

resembles  both  matter  and  energy  in  one  respect,  how- 
ever, in  that  it  can  neither  be  created  nor  destroyed. 
The  doctrine  of  the  Conservation  of  Matter,  established 
a  century  ago  by  Lavoisier,  teaches  us  that  we  can 
neither  destroy  nor  create  matter,  though  we  can  alu  r 
its  distribution,  and  its  forms  and  combinations,  in 
innumerable  ways.  The  doctrine  of  the  Conservation 
of  Energy,  which  has  been  built  up  during  the  past 
half-century  by  Helmholtz,  Thomson,  Joule,  and  Mayer, 
teaches  us  that  we  can  neither  create  nor  destroy  energy, 
though  we  may  change  it  from  one  form  to  another, 
causing  it  to  appear  as  the  energy  of  moving  bodies,,  or 
as  the  energy  of  heat,  or  as  the  static  energy  of  a  body 
which  has  been  lifted  against  gravity,  or  some  other 
attracting  force,  into  a  position  whence  it  can  run  down, 
and  where  it  has  the  potentiality  of  doing  work.  So 
also  the  doctrine  of  the  Conservation  of  Electricity,  now 
growing  into  shape,1  but  here  first  enunciated  under 
this  name,  teaches  us  that  we  can  neither  create  nor 
destroy  Electricity  though  we  may  alter  its  distribution, 
— may  cause  more  to  appear  at  one  place  and  less  at 
another, — may  change  it  from  the  condition  of  rest  to 
that  of  motion,  or  may  cause  it  to  spin  round  in  whirl- 
pools or  vortices,  which  themselves  can  attract  or  repel 
other  vortices.  According  to  this  view  all  our  electrical 
machines  and  batteries  are  merely  instruments  for  alter- 
ing the  distribution  of  Electricity  by  moving  some  of  it 

i  This  is  undoubtedly  the  outcome  of  the  ideas  of  Maxwell  and  of  Faraday 
as  to  the  nature  of  Electricity.  Since  the  above  was  written  an  elegant 
analytical  statement  of  the  "Doctrine  of  the  Conservation  of  Electricity"  has 
been  published  by  Mons.  G.  Lippmann,  who  had  independently,  and  at  an 
earlier  date,  arrived  at  the  same  view. 


viii  PREFACE. 

from  one  place  to  another,  or  for  causing  Electricity, 
when  accumulated  or  heaped  together  in  one  place,  to 
do  work  in  returning  to  its  former  level  distribution. 
Throughout  these  lessons  the  attempt  has  been  made 
to  state  the  facts  of  the  Science  in  language  consonant 
with  this  view,  but  at  the  same  time  rather  to  lead  the 
student  to  this  as  the  result  of  his  study  than  to  insist 
upon  it  dogmatically  at  the  outset. 


PREFACE 
TO  FORTY-THIRD  THOUSAND. 

Since  the  last  revision  when  Chapter  V.  on  Electro- 
magnetics was  rewritten,  few  alterations  have  been  made  ; 
but  very  brief  notices  have  been  added  of  two  most 
important  researches  of  the  year  1888,  namely  those  of 
Professor  Oliver  Lodge  on  lightning  conductors,  and 
those  of  Professor  H.  Hertz  on  the  propagation  in  space 
of  electromagnetic  waves. 

S.  P.  T. 

CITY  AND  GUILDS  TECHNICAL  COLLEGE, 
FINSBURY,  November,  1888. 


CONTENTS, 

Part  First.       . 

CHAPTER  I. 
FRICTIONAL  ELECTRICITY. 

LESSON  PAGE 

I.  Electrical  Attraction  and  Repulsion  i 

II.  Electroscopes       .         .         .  -      .         .         .  .11 

III.  Electrification  by  Induction         .         .         .  .18 

IV.  Conduction  and  Distribution  of  Electricity  .     28 
V.  Electrical  Machines      .         .         ...         .  .40 

VI.  The  Ley  den  Jar  and  other  Accumulators      .  -53 

VII.  Other  Sources  of  Electricity  -       ...  .62 

CHAPTER  II. 

.MAGNETISM. 

VIII.  Magnetic  Attraction  and  Repulsion         .  .         72 
IX.  Methods  of  Making  Magnets           .        „.  -  .       .82 

X.  Distribution  of' Magnetism     .        .      •.  .        87 

XI.  Laws  of  Magnetic  Force         »...-?-».      .  .         95 

Note  on  Ways  of  Reckoning  Angles  and  Solid- Angles    .  .          108 

Table  of  Natural  Sines  and  Tangents        .       "»''?•  .          Ill 

XII.  Terrestrial  Magnetism     .       •'.     :   V     '  V  '  .       112 


CONTENTS. 


CHAPTER  III. 
CURRENT  ELECTRICITY. 

LESSON"  TJLQt 

XIII.  Simple  Voltaic  Cells        ....  121 

XIV.  Chemical  Actions  in  the  Cell  .        »        .  131 
XV.  Voltaic  Batteries      ...        .        .  137 

XVI.  Magnetic  Actions  of  the  Current    .        .  150 

XVII.  Galvanometers         .        ;        .        .        .  161 
XVIII.  Chemical  Actions  of  the  Current.  Voltameters  171 
XIX.  Physical  and  Physiological  Effects  of  the 

Current     -.        .        .        .         .        .  180 

Part  Second. 
CHAPTER    IV. 

ELECTROSTATICS. 

XX.  Theory  of  Potential         .         .        .        .  190 

Note  on  Fundamental  and  Derived  Units     .           .  208 

XXI.  Electrometers 211 

XXII.  Specific  Inductive  Capacity,  etc.    .        .  220 

XXIII.  Phenomena  of  Discharge        .         .        .  235 

XXIV.  Atmospheric  Electricity          .        .        .  253 


CHAPTER  V. 
ELECTROMAGNETICS. 

XXV.  Theory  of  Magnetic  Potential         .        .  265 

Note  on  Magnetic  and  Electromagnetic  Units             .  28 1 
Note  on  Measurement  of  Earth's  Magnetic  Force  in 

Absolute  Units               .           .           .           .           .  284 

Note  on  Index  Notation            .           .           .           .  285 

XXVI.  Electromagnets 286 

XXVII.  Electrodynamics      .                 ...  298 

XXVIII,  Diaraagnetism         .       .       ,       ,       ,  306^ 


CONTENTS.  xi 


CHAPTER  VI. 
MEASUREMENT  OF  CURRENTS,  ETC. 

LKSSON  PACK 

XXIX.  Ohm's  Law  and  its  Consequences       .        .    307 

XXX.  Electrical  Measurements     .        .        .        .316 

Note  on  the  Ratio  of   the  Electrostatic  to  the 

Electro-magnetic  Units        .          .          .          .      326 

CHAPTER  VII. 
HEAT,  LIGHT,  AND  WORK,  FROM  ELECTRIC  CURRENTS. 

XXXI.  Heating  effects  of  Currents        .        .        .    328 
XXXII.  The  Electric  Light 333 

XXXIII.  Electromotors  (Electromagnetic  Engines)  .    340 

CHAPTER  VIII. 
THERMO-ELECTRICITY. 

XXXIV.  Thermo-Electric  Currents    ....    346 

CHAPTER  IX. 
ELECTRO  -  OPTICS. 

XXXV.  General    Relations    between     Light    and 

Electricity      ,        .        .        .        .        .353 


CONTENTS. 


CHAPTER  X. 
INDUCTION  CURRENTS  (MAGNETO-ELECTRICITY). 

LESSON  PAGE 

XXXVI.  Currents  produced  by  Induction       .  361 

XXXVII.  Magneto-electric   and    Dynamo    Electric 

Generators  .      •  -.        i  "     '.         .        .     375 

CHAPTER  XL 
ELECTRO-CHEMISTRY. 

XXXVIII.  Electrolysis  and  Electrometallurgy  .        .    387 

CHAPTER  XII. 
TELEGRAPHS  AND  TELEPHONES. 

XXXIX.  Electric  Telegraphs  .        .        .        .        .     401 
XL.  Electric  Bells,  Clocks,  and  Telephones    ,     41 1 


APPENDIX. 

PROBLEMS  AND  EXERCISES  .--.- 421 

INDEX         .        .        .        ...»        .        .        .     443 

MAGNETIC  MAP  OF  ENGLAND  AND  WALES      .     Frontispiece, 


MAGNETIC  MAP  OF  THE  UNITED  STATES..  .AN 
CANADA  / 


ELEMENTARY  LESSONS 

ON 

ELECTRICITY  &   MAGNETISM, 


CHAPTER  I. 

?R1CTIONAL   ELECTRICITY. 

LESSON  I.  —  Electrical  Attraction  and  Repulsion. 

1.  Electrical  Attraction.  —  If  you  take  a  piece  of 
sealing-wax,  or  of  resin,  or  a  glass  rod,  and  rub  it  upon 
a  piece  of  flannel  or  silk,  it  will  be  found  to  have  ac- 
quired a  property  which  it  did  not  previously  possess  : 
namely,  the  power  of  attracting  to  itself  such  light 
bodies  as  chaff,  or  dust,  or  bits  of  paper  (Fig.  i).  This 
curious  power  was  originally  discovered  to  be  a  property 
of  amber,  or,  as  the  Greeks  called  it,  vjXeKrpov,  which 
is  mentioned  by  Thales  of  Miletus  (B.C.  600),  and  by 
Theophrastus  in  his  treatise  on  Gems,  as  attracting  light 
bodies  when  rubbed.  Although  an  enormous  number  of 
substances  possess  this  property,  amber  and  jet  were  the 
only  two  in  which  its  existence  had  been  recognised  by 
the  ancients,  or  even  down  to  so  late  a  date  as  the  time 
of  Queen  Elizabeth.  About  the  year  1600,  Dr.  Gilbert 
of  Colchester  discovered  by  experiment  that  not  only 

£  B 


ELEMENTARY  LESSONS  ON         [CHAP.  I. 


amber  and  jet,  but  a  very  large  number  of  substances, 
such  as  diamond,  sapphire,  rock-crystal,  glass,  sulphur, 
sealing-wax,  resin,  etc.,  which  he  styled  eledritsj- 
possess  the  same  property.  Ever  since  his  time  the 
name  electricity  has  been  employed  to  denote  the 
agency  at  work  in  producing  these  phenomena.  Gilbert 
also  remarked  that  these  experiments  are  spoiled  by  the 
presence  of  moisture. 


Fig.  x. 

2.  A  better  way  of  observing  the  attracting  force  is 
to  employ  a  small  ball  of  elder  pith,  or  of  cork,  hung  by 
a  fine  thread  from  a  support,  as  shown  in  Fig.  2.  A 
dry^warm  glass  tube,  excited  by  rubbing  it  briskly  with 
a  silk  handkerchief,  will  attract  the  pith  ball  strongly, 
showing  that  it  is  highly  electrified.  The  most  suitable 
rubber,  if  a  stick  of  sealing-wax  is  used,  will  be  found  to 

1  " Electrica  ;  qua  attrahunt  eadem  rations  ut  electrum."— {Gilbert). 


CHAP.  I.]     ELECTRICITY  AND  MAGNETISM. 


be  flannel,  woollen  cloth,  or,  best  of  all,  fur  Boyle 
discovered  that  an  electri- 
fied body  is  itself  at- 
tracted by  one  that  has 
not  been  electrified.  This 
may  be  verified  (see  Fig. 
3)  by  rubbing  a  stick  of 
sealing-wax,  or  a  glass  rod, 
and  hanging  it  in  a  wire 
loop  at  the  end  of  a  silk 
thread.  If,  then,  the  hand 
be  held  out  towards  the 
suspended  electrified  body, 
it  will  turn  round  and  ap- 
proach the  hand.  So, 
again,  a  piece  of  silk  rib- 
bon, if  rubbed  with  warm  Flg-  2 
indiarubber,  or  even  if  drawn  between  two  pieces  of 
warm  flannel,  and  then  held  up  by  one  end,  will  be 

found  to  be  attracted 
by  objects  presented  to 
it.  If  held  near  the 
wall  of  the  room  it  will 
fly  to  it  and  stick  to  it. 
With  proper  precau- 
tions it  can  be  shown 
that  both  the  rubber 
and  the  thing  rubbed 
are  in  an  electrified 
state,  for  both  will 
attract  light  bodies ; 
but  to  show  this,  care 
must  be  taken  not  to 
handle  the  rubber  too  much.  Thus,  if  it  is  desired  lo 
show  that  when  a  piece  of  rabbit's  fur  is  rubbed  upon 
sealing-v/ax,  the  fur  becomes  also  electrified,  it  is  better 
not  to  take  the  fur  in  the  hand,  but  to  fasten  it  to  the 


Fig.  3- 


ELEMENTARY  LESSONS  ON         {CHAT.  I. 


end  of  a  glass  rod  as  a  handle.  The  reason  of  this 
precaution  will  be  explained  toward  the  close  of  this 
lesson,  and  more  fully  in  Lesson  IV. 

A  large  number  of  substances,  including  iron,  gold, 
brass,  and  all  the  metals,  when  held  in  the  hand  'tnd 
rubbed,  exhibit  no  sign  of  electrification, — that  is  to  say, 
do  not  attract  light  bodies  as  rubbed  amber  and  rubbed 
glass  do.  Gilbert  mentions  also  pearls,  marble,  agate, 
and  the  lodestone,  as  substances  not  excited  electrically 
by  rubbing  them.  Such  bodies  were,  on  that  account, 
formerly  termed  non-electrics ;  but  the  term  is  erro- 
neous, for  if  they  are  fastened  to  glass  handles  and  then 
rubbed  with  silk  or  fur,  they  behave  as  electrics. 

3.  Electrical  Repulsion.  —  When  experimenting, 
as  in  Fig.  I,  with  a  rubbed  glass  rod  and  bits  of  chopped 
paper,  or 'straw,  or  bran,  it  will  be  noticed  that  these 

little  bits  are  first  attracted 
and  fly  up  towards  the  ex- 
cited rod,  but  that,  having 
touched  it,  they  are 
speedily  repelled  and  fly 
back  to  the  table.  To 
show  this  repulsion  better, 
let  a  small  piece  of  feather 
or  down  be  hung  by  a  silk 
thread  to  a  support,  and 
let  an  electrified  glass  rod 
be  held  near  it.  It  will 
dart  towards  the  rod  and 
stick  to  it,  and  a  moment 
later  will  dart  away  from 
it,  repelled  by  an  invisible 
force  (Fig.  4),  nor  will  it 
again  dart  towards  the  rod.-  If  the  experiment  be 
repeated  with  another  feather  and  a  stick  of  sealing-wax 
rubbed  on  flannel  the  same  effects  will  occur.  But,  if 
now  the  Jhand  be  held  towards  the  feather,  it  will  rush 


CHAP.  i.J    ELECTRICITY  AND  MAGNETISM. 


toward  the  hand,  as  the  rubbed  body  in  Fig.  3  did. 
This  proves  that  the  feather,  though  it  has  not  itself 
been  rubbed,  possesses  the  property  originally  imparted  to 
the  rod  by  rubbing  it.  In  fact,  it  has  become  electrified, 
by  having  touched  an  electrified  body  which  has  given 
part  of  its  electricity  to  it.  It  would  appear  then  that 
two  bodies  electrified  with  the  same  electricity  repel  one 
another.  This  may  be  confirmed  by  a  further  experi- 
ment A  rubbed  glass  rod,  hung  up  as  in  Fig.  3,  is 
repelled  by  a  similar  rubbed  glass  rod  ;  while  a  rubbed 
stick  of  sealing-wax  is  repelled  by  a  second  rubbed  stick 
of  sealing-wax.  Another  way  of  showing  the  repulsion 
between  two  simi- 
larly electrified  bodies 
is  to  hang  a  couple 
of  small  pith -balls, 
by  thin  linen  threads 
to  a  glass  support, 
as  in  Fig.  5,  and 
then  touch  them  both 
with  a  rubbed  glass 
rod.  They  repel  one 


\ 


Fig.  5- 


another  and  fly  apart, 
instead  of  hanging 
down  side  by  side, 
while  the  near  pre- 
sence of  the  glass  rod  will  make  them  open  out  still 
wider,  for  now  it  repels  them  both.  The  self-repulsion 
of  the  parts  of  an  electrified  body  is  beautifully  illustrated 
by  the  experiment  of  electrifying  a  soap-bubble,  which 
expands  when  electrified. 

4.  Two  kinds  of  Electrification.  —  Electrified 
bodies  do  not.,  however,  always  repel  one  another.  The 
feather  which  (see  Fig.  4)  has  been  touched  by  a  rubbed 
glass  rod.  and  which  in  consequence  is  repelled  from 
the  rubbed  glass,  will  be  attmted  if  a  stick  of  rubbed 
sealing-wax  be  presented  to  it;  and  conversely,  if  the 


6  ELEMENTARY  LESSONS  ON         [CHAP;  I. 

feather  has  been  first  electrified  by  touching  it  with  the 
rubbed  sealing-wax,  it  will  be  attracted  to  a  rubbed  glass 
rod,  though  repelled  by  the  rubbed  wax.  So,  again,  a 
rubbed  glass  rod  suspended  as  in  Fig.  3  will  be  attracted 
by  a  rubbed  piece  of  sealing-wax,  or  resin,  or  amber, 
though  repelled  by  a  rubbed  piece  of  glass.  The  two 
pith-balls  touched  (as  in  Fig.  5)  with  a  rubbed  glass 
rod  fly  from  one  another  by  repulsion,  and,  as  we  have 
seen,  fly  wider  asunder  when  the  excitetl  glass  rod  is 
held  near  them  ;  yet  they  fall  nearer  together  when  a 
rubbed  piece  of  sealing-wax  is  held  under  them,  being 
attracted  by  it.  Symmer  first  observed  such  phenomena 
as  these,  and  they  were  independently  discovered  by  Du 
Fay,  who  suggested  in  explanation  of  them  that  there 
were  two  different  kinds  of  electricity  which  attracted 
one  another  while  each  repelled  itself.  The  electricity 
produced  on  glass  by  rubbing  it  with  silk  he  called 
vitreous  electricity,  supposing,  though  erroneously,  that 
glass  could  yield  no  other  kind ;  and  the  electricity 
excited  in  such  substances  as  sealing-wax,  resin,  shellac, 
indiarubber,  and  amber,  by  rubbing  them  on  wool  01 
flannel,  he  termed  resinous  electricity.  The  kind  oi 
electricity  produced  is,  however,  found  to  depend  not  only 
on  the  thing  rubbed  but  on  the  rubber  also ;  for  glass 
yields  "  resinous "  electricity  when  rubbed  with  a  cat's 
skin,  and  resin  yields  "  vitreous  "  electricity  if  rubbed 
with  a  soft  amalgam  of  tin  and  mercury  spread  on 
leather.  Hence  these  names  have  been  abandoned  in 
favour  of  the  more  appropriate  terms  introduced  by 
Franklin,  who  called  the  electricity  excited  upon  glass  by 
rubbing  it  with  silk  positive  electricity,  and  that  produced 
on  resinous  bodies  by  friction  with  wool  or  fur,  negative 
electricity.  The  observations  of  Symmer  and  Du  Fay  may 
therefore  be  stated  as  follows  : — Two  positively  electrified 
bodies  repel  one  another:  two  negatively  electrified  bodies 
repel  one  another :  but  a  positively  electrified  body  and 
a  negatively  electrified  body  attract  one  another, 


CHAP,  i.]      ELECTRICITY  AND  MAGNETISM.  7 

5.  Simultaneous  production  of  both  Electrical 
States. — Neither   kind   of    electrification    is    produced 
alone ;  there  is  always  an  equal  quantity  of  both  kinds 
produced ;    one   kind    appearing   on    the    thing   rubbed 
and  an  equal  amount  of  the  other  kind  on  the  rubber. 
The  clearest  proof  that  these  amounts  are  equal  can  be 
given  in  some  cases.      For  it  is  found  that  if  both  the  — 
electricity  of  the  rubber  and  the  +  electricity  of  the  thing 
rubbed  be  imparted  to  a  third  body,  that  third  body  will 
show  no  electrification  at  all,  the  two  equal  and  opposite 
electrifications  having  exactly  neutralised  each  other. 

In  the  following  list  the  bodies  are  arranged  in  such 
an  order  that  if  any  two  be  rubbed  together  the  one 
which  stands  earlier  in  the  series  becomes  positively 
electrified,  and  the  one  that  stands  later  negatively 
electrified : — Fur,  wool,  ivory,  glass,  silk,  metals,  sul- 
phur, indiarubber,  gitttapercha,  collodion. 

6.  Theories  of  Electricity. — Several  theories,  have 
been  advanced  to  account  for  these  phenomena,  but  all 
are  more  or  less  unsatisfactory.     Symmer  proposed  a 
•'  two-fluid  "  theory,  according  to  which  there  are  two 
imponderable    electric    fluids    of  opposite  kinds,   which 
neutralise  one  another  when  they  combine,  and  which 
exist   combined   in   equal   quantities   in   all   bodies  until 
their  condition  is  disturbed  by  friction.      A  modification 
of  this  theory   was   made   by   Franklin,   who   proposed 
instead   a    "one-fluid"   theory,    according   to    which 
there  is  a  single  electric  fluid  distributed  usually  uniformly 
in  all  bodies,  but  which,  when  they  are  subjected  to  friction, 
distributes  itself  unequally  between  the  rubber  and  the 
thing  rubbed,  one  having  more  of  the  fluid,  the  other 
less,  than  the  average.     Hence  the  terms  positive  and 
negative,  which  are   still   retained  :  that  body  which  is 
supposed  to  have  an  excess  being   said  to  be   charged 
with  positive  electricity  (usually  denoted  by  the  plus  sign 
+  ),  while  that  which  is  supposed  to  have  less  is  said  to 
be  charged  with  negative  electricity  (and  is  denoted  by 


8  ELEMENTARY  LESSONS  ON          [CHAP.  i. 

the  minus  sign  -  ).  These  terms  are,  however,  purely 
arbitrary,  for  in  the  present  state  of  science  we  do  not 
know  which  of  these  two  states  really  means  more  and 
which  means  less.  It  is,  however,  quite  certain  that 
electricity  is  not  a  material  fluid,  whatever  else  it 
may  be.  For  while  it  resembles  a  fluid  in  its  property 
of  apparently  flowing  from  one  point  to  another,  it  differs 
from  every  known  fluid  in  almost  ever)'  other  respect. 
It  possesses  no  weight ;  it  repels  itself.  -It  is,  moreover, 
quite  impossible  to  conceive  of  two  fluids  whose  proper- 
ties should  in  every  respect  be  the  precise  opposites  of 
one  another.  For  these  reasons'  it  is  clearly  misleading 
to  speak  of  an  electric  fluid  or  fluids,  however  convenient 
the  term  may  seem  to  be.  Another  theory,  usually  known 
as  the  molecular  theory  of  electricity,  and  first  dis- 
tinctly upheld  by  Faraday,  supposes  that  electrical  states 
are  the  result  of  certain  peculiar  conditions  of  the  mole- 
cules of  the  bodies  that  have  been  rubbed,  or  of  the 
"aether"  which  is  believed  to  surround  the  molecules. 
There  is  much  to  be  said  in  favour  of  this  hypothesis, 
but  it  has  not  yet  been  proven.  In  these  lessons,  there- 
fore, we  shall  avoid  as  far  as  possible  all  theories,  and 
shall  be  content  to  use  the  term  electricity. 

7.  Charge. — The  quantity  of  electrification  of  either 
kind  produced  by  friction  or  other  means  upon  the  surface 
of  a  body  is  spoken  of  as  a  charge,  and  a  body  when 
electrified  is  said  to  be  charged.  It  is  clear  that  there 
may  be  charges  of  different  values  as  well  as  of  either 
kind.  When  the  charge  of  electricity  is  removed  from 
a  charged  body  it  is  said  to  be  discharged.  Good 
conductors  of  electricity  are  instantaneously  discharged 
if  touched  by  the  hand  or  by  any  conductor  in  contact 
with  the  ground,  the  charge  thus  finding  a  means  of 
escaping  to  earth.  A  body  that  is  not  a  good  conductor 
may  be  icadily  discharged  by  passing  it  rapidly  through  the 
flame  of  a  spii it-lamp  or  a  candle  ;  foi  the  flame  instantly 
carries  off  the  electricity  and  dissipates  it  in  the  air. 


CHAP,  i.j    ELECTRICITY  AND  MAGNETISM.  9 

Electricity  may  either  reside  upon  the  surface  of  bodies 
as*  a  c}iarge^  or  flow  through  their  substance  as  a 
current.  That  branch  of  the  science  which  treats  of 
the  laws  of  the  charges  upon  the  surface  of  bodies  is 
termed  electrostatics,  and  is  dealt  with  in  Chapter 
IV.  The  branch  of  the  subject  which  treats  of  the  flow 
of  electricity  in  currents  is  dealt  with  in  Chapter  III.,  and 
other  later  portions  of  this  book. 

i-    8.  Conductors  and  Insulators. — The  term  "con- 
ductors," used  above,  is  applied  to  those  bodies  which 
readily  allow  electricity  to  flow  through  them.     Roughly 
speaking  bodies  may  be  divided  into  two  classes — those 
which  conduct  and  those  which  do  not ;    though    very 
many  substances  are  partial  conductors,  and  cannot  well 
be  classed  in  either  category.      All  the  metals  conduct 
well  ;    the  human    body  conducts,  and   so    does  water. 
On  the  other  hand  glass,  sealing-wax,  silk,  shellac,  gutta- 
percha,  indiarubber,    resin,    fatty    substances  generally, 
and  the  air,  are  "  non-conductors."     On  this  account 
these  substances  are  used  to  make  supports  and  handles 
for  electrical  apparatus  where   it  is  important  that  the 
electricity  should  not  leak  away ;  hence  they  are  some- 
times called  insulators  or  isolators.     Faraday  termed 
them  dielectrics.     We  have  remarked  above  that  Gil- 
bert gave  the  name  of  non-electrics  to  those  substances 
which,  like  the  metals,  yield  no  sign  of  electrification  when 
held  in  the  hand  and  rubbed.     We  now  know  the  reason 
why  they  show  no  electrification  ;  for,  being  good  conduct- 
ors, the  electricity  flows  away  as  fast  as  it  is  generated. 
The  observation  of  Gilbert    that   electrical  experiments 
fail  in  damp  weather  is  also  explained  by  the  knowledge 
that  water  is  a  conductor,  the  film  of  moisture  on  the 
surface  of  damp  bodies  causing  the  electricity  produced 
by  friction  to  leak  away  as  fast  as  it  is  generated. 

9.  Other  electrical  effects. — The  production  of 
electricity  by  friction  is  attested  by  other  effects  than 
those  of  attraction  and  repulsion,  which  hitherto  we  have 


io  ELEMENTARY  LESSONS  ON         [CHA?.  i 

assumed  to  be  the  test  of  the  presence  of  electricity. 
Olio  von  Guericke  first  observed  that  sparks  and  flashes 
of  light  could  be  obtained  from  highly  electrified  bodies  at 
the  moment  when  they  were  discharged.  Such  sparks  are 
usually  accompanied  by  a  snapping  sound,  suggesting  on  a 
small  scale  the  thunder  accompanying  the  lightning  spark, 
as  was  remarked  by  Newton  and  other  early  observers. 
Pale  flashes  of  light  are  also  produced  by  the  discharge 
of  electricity  through  tubes  partially  exhausted  of  air  by 
the  air-pump.  Other  effects  will  be  noticed  in  due  course. 
IO.  Other  Sources  of  Electrification. — The  stu- 
dent must  be  reminded  that  friction  is  by  no  means  the 
only  source  of  electricity.  The  other  sources,  per- 
cussion, compression,  heat,  chemical  action,  physiological 
action,  contact  of  metals,  etc.,  will  be  treated  of  in  Lesson 
VII.  We  will  simply  remark  here  that  friction  between 
two  different  substances  always  produces  electrical 
separation,  no  matter  what  the  substances  may  be. 
Synimer  observed  the  production  of  electricity  when  a 
silk  stocking  was  drawn  over  a  woollen  one,  though 
woollen  rubbed  upon  woollen,  or  silk  rubbed  upon  silk, 
produces  no  electrical  effect.  If,  however,  a  piece  of 
rough  glass  be  rubbed  on  a  piece  of  smooth  glass, 
electrification  is  observed ;  and  indeed  the  conditions  of 
the  surface  play  a  very  important  part  in  the  production 
of  electricity  by  friction.  In  general,  of  two  bodies 
thus  rubbed  together,  that  one  becomes  negatively 
electrical  whose  particles  are  the  more  easily  removed 
by  friction.  Differences  of  temperature  also  affect  the 
electrical  conditions  of  bodies,  a  warm  body  being  usually 
negative  when  rubbed  on  a  cold  piece  of  the  same  sub- 
stance. Pdclet  found  the  degree  of  electrification  produced 
by  rubbing  two  substances  together  to  be  independent  of 
the  pressure  and  of  the  size  of  the  surfaces  in  contact, 
but  depended  on  the  materials  and  on  the  velocity  with 
which  they  moved  over  one  another.  Rolling  friction 
and  slicing  friction  produced  equal  effects.  The  quantity 


CHAP,  i.]     ELECTRICITY  AND  MAGNETISM  it1 

IT 

of  electrification  produced  is,  however,  not  proportional 
to  the  amount  of  the  actual  mechanical  friction  ;  hence 
it  appears  doubtful  whether  friction  is  truly  the  cause  of 
the  electrification  Indeed,  it  is  probable  that  the  true 
cause  is  the  contact  of  dissimilar  substances  (see  Art. 
73),  and  that  when  on  contact  two  particles  have 
assumed  opposite  electrical  states,  one  being  +  the 
other  -  ,  it  is  necessary  to  draw  them  apart  before  their 
respective  electrifications  can  be  observed.  Electrical 
machines  are  therefore  machines  for  bringing  dissimilar 
substances  into  intimate  contact,  and  then  drawing  apart 
the  particles  that  have  touched  one  another  and  become 
electrical. 

L  ESSON   II. — Electroscopes^ 

11.  Simple    Electroscopes.  —  An    instrument    for 
detecting    whether   a    body    is    electrified    or    not,    and 
whether    the   electrification    is    positive  or    negative,    is 
termed   an    Electroscope.      The    feather    which    was 
attracted  or  repelled,  and  the  two  pith  balls  which  flew 
apart,  as  we,  found    in    Lesson    L,  are   in  reality  simple 
electroscopes.     There  are,  however,  a  number  of  pieces 
of  apparatus  better  adapted  for  this  particular  purpose, 
some  of  which  we  will  describe. 

12.  Straw -Needle    Electroscope. —  The    earliest 
electroscope  was  that  devised  by  Dr.  Gilbert,  and  shown 
in  Fig.  6,  which  consists  of  a  stiff  straw  balanced  lightly 


Fig.  6. 

upon  a  sharp  point.     A  thin  strip  of  brass  or  wood,  or 
even  a  goose  quill,  balanced  upon  a  sewing  needle,  will 


12  ELEMENTARY  LESSONS  ON         [CHAP,  if 

serve  equally  well.  When  an  electrified  body  is  held  near 
the  electroscope  it  is  attracted  and  turned  round,  and  will 
thus 'indicate  the  presence  of  quantities  of  electricity  far 
too  small  to  attract  bits  of  paper  from  a  table. 

13.  G-old-Leaf  Electroscope. — A  still  more  sensi- 
tive instrument  is  the  G-old-Leaf  Electroscope  In- 
vented by  Bennet,  and  shown  hi  Fig.  7.  We  have 
seen  how  two  pith- balls  when  similarly  electrified  repel 
one  another  and  stand  apart,  the  force  of  gravity  being 
partly  overcome  by  the  force  of  the  electric  repulsion. 


Fig.  7. 

A  couple  of  narrow  strips  of  the  thinnest  tissue  paper, 
hung  upon  a  support,  will  behave  similarly  when  electri- 
fied. But  the  best  results  are  obtained  with  two  strips 
of  gold-leaf,  which,  being  excessively  thin,  is  much 
lighter  than  the  thinnest  paper.  The  Gold-Leaf  Electro- 
scope is  conveniently  made  by  suspending  the  two  leaves 
within  a  wide-mouthed  glass  jar,  which  both  serves  to 


CHAP.  I.]    ELECTRICITY  AND  MAGNETISM.  13 

protect  them  from  draughts  of  air  and  to  support  thein 
from  contact  with  the  ground.  Through  the  cork,  which 
should  be  varnished  with  shellac  or  with  paraffin  wax,  is 
pushed  a  bit  of  glass  tube,  also  varnished.  Through  this 
passes  a  stiff  brass  wire,  the  lower  end  of  which  is  bent 
at  a  right  angle  to  receive  the  two  strips  of  gold-leaf, 
while  the  upper  supports  a  flat  plate  of  metal,  or  may  be 
furnished  with  a  brass  knob.  When  kept  dry  and  free 
from  dust  it  will  indicate  excessively  small  quantities  of 
electricity.  A  rubbed  glass  rod,  even  while  two  or  three 
feet  from  the  instrument,  will  cause  the  leaves  to  repel 
one  another.  The  chips  produced  by  sharpening  a  pencil, 
falling  on  the  electroscope  top,  are  seen  to  be  electrified. 
If  the  knob  be  even  brushed  with  a  small  camel's  hair 
brush,  the  slight  friction  produces  a  perceptible  effect. 
With  this  instrument  all  kinds  of  friction  can  be  shown 
to  produce  electrification.  Let  a  person,  standing  upon 
an  insulating  support, — such  as  a  stool  with  glass  legs, 
or  a  board  supported  on  four  glass  tumblers, — be  briskly 
struck  with  a  silk  handkerchief,  or  with  a  fox's  tail,  or 
even  brushed  with  a  clothes'  brush,  he  will  be  electrified, 
as  will  be  indicated  by  the  electroscope  if  he  place  one 
hand  on  the  knob  at  the  top  of  it.  The  Gold-Leaf 
Electroscope  can  further  be  used  to  indicate  the  kind  of 
electricity  on  an  excited  body.  Thus,  suppose  we  rubbed 
a  piece  of  brown  paper  with  a  piece  of  indiarubber  and 
desired  to  find  out  whether  the  electrification  excited  on 
the  paper  was  +  or  —  ,  we  should  proceed  as  follows  : — 
First  charge  the  gold  leaves  of  the  electroscope  by 
touching  the  knob  with  a  glass  rod  rubbed  on  silk. 
The  leaves  diverge,  being  electrified  with  +  electrifi- 
cation. When  they  are  thus  charged  the  approach  of 
a  body  which  is  positively  electrified  will  cause  them  to 
diverge  still  more  widely  ;  while,  on  the  approach  of  one 
negatively  electrified,  they  will  tend  to  close  together. 
If  now  the  brown  paper  be  brought  near  the  electroscope, 
the  leaves  will  be  seen  to  diverge  more.  Droving  the 


14  ELEMENTARY  LESSONS  ON        [CHAP.  I 

electrification  of  the  paper  to  be  of  the  same  kind  as 
that  with  which  the  electroscope  is  charged,  or  positive. 
The  Gold-Leaf  Electroscope  will  also  indicate  roughly 
the  amount  of  electricity  on  a  body  placed  in  contact 
with  it,  for  the  gold  leaves  open  out  more  widely  when 
the  quantity  of  electricity  thus  imparted  to  them  is  greater. 
For  exact  measurement,  however,  of  the  amounts  of 
electricity  thus  present,  recourse  must  be  had  to  the  instru- 
ments known  as  Electrometers,  described  in  Lesson  XXI. 
In  another  form  of  electroscope  (Bohnenberger's)  a 
single  gold  leaf  is  used,  and  is  suspended  between  two 
metallic  plates,  one  of  which  can  be  positively,  the  other 
negatively  electrified,  by  placing  them  in  communication 
with  the  poles  of  a  "  dry  pile  "  (Art.  182).  If  the  gold 
leaf  be  charged  positively  or  negatively  it  will  be 
attracted  to  one  side  and  repelled  from  the  other, 
according  to  the  law  of  attraction  and  repulsion  men- 
tioned in  Art.  4. 

14.  Henley's  Quadrant  Electroscope.  —  The 
Quadrant  Electroscope  is  sometimes  employed  as  an 
indicator  for  large  charges  of  electricity.  It  consists  oi 
a  pith  ball  at  the  end  of  a  light 
arm  fixed  on  a  pivot  to  an  upright. 
When  the  whole  is  electrified  the 
pith-ball  is  repelled  from  the  up- 
right and  flies  out  at  an  angle, 
indicated  on  a  graduated  scale  or 
quadrant  behind  it.  Its  usual  form 
is  shown  in  Fig.  8.  This  little 
electroscope,  which  is  seldom 
used  except  to  show  whether  an 
electric  machine  or  a  Leyden 
battery  is  charged,  must  en  no 
Flg<  8i  account  be  confused  with  the  deli- 

cate "Quadrant  Electrometer "  described  in  Lesson 
XXL,  whose  object  is  to  measure  very  small  charges 
of  electricity — not  to  indicate  large  ones. 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM. 


15.  The  Torsion  Balance. — Although  more  pro- 
perly an  Electrometer  than  a  mere  Electroscope ',  it 
will  >  be  most  convenient  to  describe  here  the  instrument 
known  as  the  Torsion 
Balance.  (Fig.  9.)  This 
instrument  serves  to 
measure  the  force  of  the 
repulsion  between  two 
similarly  electrified 
bodies,  by  balancing  the 
force  of  this  repulsion 
against  the  force  exerted 
by  a  fine  wire  in  untwist- 
ing itself  after  it  has  been 
twisted.  The  torsion 
balance  consists  of  a 
light  arm  or  lever  of 
shellac  suspended  within 
a  cylindrical  glass  case 


Fig.  9. 


by  means  of  a  fine  silver  wire.  At  one  end  this  lever  is 
furnished  with  a  gilt  pith-ball,  n.  The  upper  end  of  the 
siher  wire  is  fastened  to  a  brass  top,  upon  which  a  circle, 
divided  into  degrees,  is  cut.  This  top  can  be  turned 
round  in  the  tube  which  supports  it,  and  is  known  as  the 
torsion-head.  Through  an  aperture  in  the  cover  there 
can  be  introduced  a  second  gilt  pith -ball  tnt  fixed  to 
the  end  of  a  vertical  glass  rod  a.  Round  the  glass  case, 
at  the  level  of  the  pith-balls,  a  circle  is  drawn,  and 
divided  also  into  degrees. 

In  using  the  torsion  balance  to  measure  the  amount 
of  a  charge  of  electricity,  the  following  method  is 
adopted : — First,  the  torsion-head  is  turned  round  until 
the  t\\o  pith-balls  m  and  n  just  touch  one  another. 
Then  the  glass  rod  a  is  taken  out,  and  the  charge  of 
electricity  to  be  measured  is  imparted  to  the  ball  #/, 
which  is  then  replaced  in  the  balance.  As  soon  as  ;// 
and  n  touch  one  another,  part  of  the  charge  passes  from 


16  ELEMENTARY  LESSONS  ON         [CHAP.  t. 

m  to  #,  and  they  repel  one  another  because  they  are 
then  similarly  electrified.  The  ball ;/,  therefore,  is  driven 
round  and  twists  the  wire  up  to  a  certain  extent.  The 
force  of  repulsion  becomes  less  and  less  as  n  gets 
farther  and  farther  from  m ;  but  the  force  of  the  twis; 
gets  greater  and  greater  the  more  the  wire  is  twisted. 
Hence  these  two  forces  will  balance  one  another  when 
the  balls  are  separated  by  a  certain  distance,  and  it  is 
clear  that  a  large  charge  of  electricity  will  repel  the  ball 
«  with  a  greater  force  than  a  lesser  charge  would. 
The  distance  through  which  the  ball  is  repelled  is  read 
off  not  in  inches  but  in  angular  degrees  of  the  scale. 
When  a  wire  is  twisted,  the  force  with  which  it  tends  to 
untwist  is  precisely  proportional  to  the  amount  of  the 
twist.  The  force  required  to  twist  the  wire  ten  degrees 
is  just  ten  times  as  great  as  the  force  required  to  twist 
it  one  degree.  In  other  words,  the  force  of  torsion  is 
proportional  to  the  angle  of  torsion.  The  angular 
distance  between  the  two  balls  is,  when  they  are  not 
very  widely  separated,  very  nearly  proportional  to  the 
actual  straight  distance  between  them,  and  represents 
the  force  exerted  between  electrified  balls  at  thai 
distance  apart.  The  student  must,  however,  carefully 
distinguish  between  the  measurement  of  the  force  and 
the  measurement  of  the  actual  quantity  of  electricity 
with  which  the  instrument  is  charged.  For  the  force 
exerted  between  the  electrified  balls  will  vary  at  different 
distances  according  to  a  particular  law  known  as  the 
"  law  of  inverse  squares,"  which  requires  to  be  carefully 
explained. 

16.  The  Law  of  Inverse  Squares.  —  Coulomb 
proved,  by  means  of  the  Torsion  Balance,  that  the  force 
exerted  between  two  small  electrified  bodies  varies 
inversely  as  the  square  of  the  distance  between  thena 
when  the  distance  is  varied.  Thus,  suppose  two  electri- 
fied bodies  one  inch  apart  repel  one  another  with  a 
certain  force,  at  a  distance  of  two  inches  the  force  will 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM. 


be  found  to  be  only  one  quarter  as  great  as  the  force 
at  one  inch ;  and  at  ten  inches  it  will  ba  only  j~th 
part  as  great  as  at  one  inch.  This  law  is  proved  by  the 
following  experiment  with  the  torsion  balance.  The 
two  scales  were  adjusted  to  o°,  and  a  certain  charge  was 
then  imparted  to  the  balls.  The  ball  n  was  repelled 
round  to  a  distance  of  36°.  The  twist  on  the  wire 
between  its  upper  and  lower  ends  was  also  36°,  or  the 
force  of  the  repulsion  was  thirty-six  times  as  great  as  the 
force  required  to  twist  the  wire  by  i°.  The  torsion-head 
was  now  turned  round  so  as  to  twist  the  thread  at  the 
top  and  force  the  ball  n  nearer  to  M,  and  was  turned 
round  until  the  distance  between  n  and  m  was  halved. 
To  bring  down  this  distance  from  36°  to  18°,  it  was 
found  needful  to  twist  the  torsion -head  through  126°. 
The  total  twist  between  the  upper  and  lower  ends  of  the 
wire  was  now  126°  +  18°,  or  144°;  and  the  force  was 
144  times  as  great  as  that  force  which  would  twist  the 
wire  i°.  But  144  is  four  times  as  great  as  36 ;  hence 
we  see  that  while  the  distance  had  been  reduced  to  one 
/la!/,  the  force  between  the  balls  had  become  four 
times  as  great.  Had  we  reduced  the  distance  to  one 
quarter,  or  9°,  the  total  torsion  would  have  been  found 
to  be  576°,  or  sixteen  times  as  great;  proving  the 
force  to  vary  inversely  as  the  square  of  the 
distance. 

In  practice  it  requires  great  experience  and  skill  to 
obtain  results  as  exact  as  this,  for  there  are  many 
sources  of  inaccuracy  in  the  instrument.  >The  balls 
must  be  very  small,  in  proportion  to  the  distances  between 
them.  The  charges  of  electricity  on  the  balls  are  found, 
moreover,  to  become  gradually  less  and  less,  as  if  the 
electricity  leaked  away  into  the  air.  This  loss  is  less 
if  tlie  apparatus  be  quite  dry.  It  is  therefore  usual  to 
dry  the  interior  by  placing  inside  the  case  a  cup  con- 
taining either  chloride  of  calcium,  or  pumice  stone 
soaked  with  strong  sulphuric  acid,  to  absorb  the  moisture, 


i8  ELEMENTARY  LESSONS  ON          [CHAP,  i. 

Before  leaving  the  subject  of  electric  forces,  it  may  be 
well  to  mention  that  the  force  of  attraction  between 
two  oppositely  electrified  bodies  varies  also  inversely  as 
the  square  of  the  distance  between  them.  And  in  every 
case,  whether  of  attraction  or  repulsion,  the  force  at  any 
given  distance  is  proportional  to  the  product  of  the 
two  quantities  of  electricity  on  the  bodies.  Thus,  if 
we  had  separately  given  a  charge  of  2  to  the  ball  m  and 
a  charge  of  3  to  the  ball  n,  the  force  between  them  will 
be  3  x  2  «=:  6  times  as  great  .as  if  each  had  had  a 
charge  of  I  given  to  it. 

17.  Unit  quantity  of  Electricity.  —  In  conse- 
quence of  these  laws  of  attraction  and  repulsion,  it  is 
found  most  convenient  to  adopt  the  following  definition 
for  that  quantity  of  electricity  which  we  take  for  a  unit  or 
standard  by  which  to  measure  other  quantities  of  elec- 
tricity. One  Unit  of  Electricity  is  that  quantity  which^ 
when  placed  at  a  distance  of  one  centimetre  in  air  from 
a  similar  and  equal  qitantity,  repels  it  with  a  force  of 
one  dyne.  Further  information  about  the  measure- 
ment of  electrical  quantities  is  given  in  Lessons  XX. 
and  XXI 


LESSON   III. — Electrification  by  Induction. 

18.  We  have  now  learned  how  two  charged  bodies 
may  attract  or  repel  one  another.  It  is  sometimes  said 
that  it  is  the  electricities  in  the  bodies  which  attract  or 
repel  one  another ;  but  as  electricity  is  not  known  to 
exist  except  in  or  on  material  bodies,  the  proof  that  it 
is  the  electricities  themselves  which  are  attracted  is  only 
indirect.  Nevertheless  there  are  certain  matters  which 
support  this  view,  one  of  these  being  the  electric  influ- 
ence exerted  by  an  electrified  body  upon  one  not 
electrified. 

Suppose  we  rub  a  ball  of  glass  with  silk  to  electrify  it, 


CHAPTI.]  .ELECTRICITY  AND  MAGNETISM. 


and  hold  it  near  to  a  body  that  has  not  been  electrified, 
what  will  occur  ?  We  take  for  this  experiment  the 
apparatus  shown  in  Fig.  10,  consisting  of  a  long 
sausage -shaped  piece  of  metal,  either  hollow  or  solid, 
held  upon  a  glass  support.  This  "conductor,"  so  called 
because  it  is  made  of  metal  which  permits  electricity  to 
pass  freely  through  it  or  over  its  surface,  is  supported  on 
glass  to  prevent  the  escape  of  electricity  to  the  earth, 
glass  being  a.  non-conductor.  The  presence  of  the 
positive  electricity  of  the  glass  ball  near  this  conductor 
is  found  to  induce  electricity  on  the  conductor,  which, 


Fig.  10. 


although  it  has  not  been  rubbed  itself,  will  be  found  to 
behave  at  its  two  ends  as  an  electrified  body.  The 
ends  of  the  conductor  will  attract  little  bits  of  paper; 
and  if  pith -balls  be  hung  to  the  ends  they  are  found 
to  be  repelled.  It  will,  however,  be  found  that  the 
middle  region  of  the  long -shaped  conductor  will  give 
no  sign  of  any  electrification.  Further  examination  will 
show  that  the  two  electrifications  on  the  ends  of  the  con- 
ductor are  of  opposite  kinds,  that  nearest  the  excited 
glass  ball  being  a  negative  charge,  and  that  at  the 
farthest  end  being  an  eaual  charge,  but  of  positive 


20  ELEMENTARY  LESSONS  ON        [CHAP.  1. 

sign.  It  appears  then  that  a  positive  charge  attracts 
negative  and  repels  positive,  and  that  this  influence  can 
be  exerted  at  a  distance  from  a  body.  If  we  had  begun 
with  a  charge  of  negative  electrification  upon  a  stick  of 
sealing-wax,  the  presence  of  the  negative  charge  near  the 
conductor  would  have  induced  a  positive  charge  on  the 
near  end,  and  negative  on  the  far  end.  This  action, 
discovered  in  1753  by  John  Canton,  is  spoken  of  as 
electric  induction,  or  influence.  It  'will  take  place 
across  a  considerable  distance.  Even  if  a  large  sheet 
of  glass  be  placed  between,  the  same  effect  will  be 
produced.  When  the  electrified  body  is  removed  both 
the  charges  disappear  and  leave  no  trace  behind,  and 
the  glass  ball  is  found  to  be  just  as  much  electrified  as 
before  ;  it  has  parted  with  none  of  its  own  charge.  It 
will  be  remembered  that  on  one  theory  a  body  charged 
positively  is  regarded  as  having  more  -electricity  than 
the  things  round  it,  while  one  with  a  negative  charge 
is  regarded  as  having  less.  According  to  this  view 
it  would  appear  that  when  a  body  (such  as  the  + 
electrified  glass  ball)  having  more  electricity  than 
things  around  it  is  placed  near  an  insulated  conductor, 
the  uniform  distribution  of  electricity  in  that  conductor 
is  disturbed,  the  electricity  flowing  away  from  that  end 
which  is  near  the  +  body,  leaving  less  than  usual  at 
that  end,  and  producing  more  than  usual  at  the  other 
end.  This  view  of  things  will  account  for  the  disappear- 
ance &f  all  signs  of  electrification  when  the  electrified 
body  is  removed,  for  then  the  conductor  returns  to  its 
former  condition  ;  and  being  neither  more  nor  less  elec- 
trified than  all  the' objects  around  on  the  surface  of  the 
earth,  will  show  neither  positive  nor  negative  charge. 

19.  If  the  conductor  be  made  in  two  parts,  so  that 
while  under  the  inductive  influence  of  the  electrified 
body  they  can  be  separated,  then  on  the  removal  of  the 
electrified  body  the  two  charges  can  no  longer  return 
to  neutralise  one  another,  but  remain  each  on  their  own 


CHAP,  i.j    ELECTRICITY  AND  MAGNETISM.  21 

portion    of  tho   conductor,  and    may  be   examined   at 
leisure. 

If  the  conductor  be  not  insulated  on  glass  supports, 
but  placed  in  contact  with  the  ground,  that  end  only 
which  is  nearest  the  electrified  body  will  be  found  to  be 
electrified.  The  repelled  electricity  is  indeed  repelled 
as  far  as  possible  —  into  the  earth.  One  kind  of  elec- 
trification only  is  under  these  circumstances  to  be  found, 
namely,  the  opposite  kind  to  that  of  the  excited  body, 
whichever  this  may  be.  The  same  effect  occurs  in  this 
case  as  if  an  electrified  body  had  the  power  of  attracting 
up  the  opposite  kind  of  charge  out  of  the  earth,  though 
the  former  way  of  regarding  matters  is  more  correct. 
*»  The  quantity  of  the  two  charges  thus  separated  by 
induction  on  such  a  conductor  in  the  presence  of  a 
charge  of  electricity,  depends  upon  the  amount  of  the 
charge,  and  upon  the  distance  of  the  charged  body  from 
the  conductor.  A  highly  electrified  glass  rod  will 
produce  a  greater  inductive  effect  than  a  less  highly 
electrified  one ;  and  it  produces  a  greater  effect  as  it  is 
brought  nearer  and  nearer.  The  utmost  it  can  do  will 
be  to  induce  on  the  near  end  a  negative  charge  equal 
in  amount  to  its  own  positive  charge,  and  a  similar 
amount  of  positive  electricity  at  the  far  end  ;  but  usually, 
before  the  electrified  body  can  be  brought  so  near  as  to 
do  this,  something  else  occurs  which  entirely  alters  the 
condition  of  things.  As  the  electrified  body  is  brought 
nearer  and  nearer,  the  charges  of  opposite  sign  on  the 
two  opposed  surfaces  attract  one  another  more  and 
more  strongly  and  accumulate  more  and  more  densely, 
until,  as  the  electrified  body  approaches  very  near,  a  spark 
is  seen  to  dart  across,  the  two  charges  thus  rushing 
together  to  neutralise  one  another,  leaving  the  induced 
charge  of  positive  electricity,  which  was  formerly  repelled 
to  the  other  end  of  the  conductor,  as  a  permanent  charge 
after  the  electrified  body  has  been  removed. 

2O.    We   are    now   able    to    apply  the    principle    of 


22  ELEMENTARY  LESSONS  ON        [CHAP,  t 

•  '  i 

induction  to  explain  why  an  electrified  body  should 
attract  things  that  have  not  been  electrified  at  all.  Let 
a  light  ball  be  suspended  by  a  silk  thread  (Fig.  1 1 ),  and 
a  rubbed  glass  rod  held  near  it.  The  positive  charge 
of  the  glass  will  induce  a  negative  charge  on  the  near  side, 

and  an  equal  amount  of  posi- 
tive electrification  on  the  farther 
side,  of  the  ball.  The  nearer 
half  of  the  ball  will  therefore 
be  attracted,  and  the  farther 
half  repelled ;  but  the  attraction 
will  be  stronger  than  the  repul- 
sion, because  the  attracted  elec- 
tricity is  nearer  than  the  repelled.  Hence  on  the  whole 
the  ball  will  be  attracted.  It  can  easily  be  observed 
that  if  a  ball  of  non-conducting  substance,  such  as  wax, 
be  employed,  it  is  not  attracted  so  much  as  a  ball  of 
conducting  material.  This  in  itself  proves  that  induction 
really  precedes  attraction. 

21.  Inductive  capacity. — We  have  assumed  up  to 
this  point  that  electricity  could  act  at  a  distance,  and 
could  produce  these  effects  of  induction  without  any 
intervening  means  of  communication.  This,  however, 
is  not  the  case,  for  Faraday  discovered  that  the  air  in 
between  the  electrified  body  and  the  conductor  played  a 
very  important  part  in  the  production  of  these  actions. 
Had  some  other  substance,  such  as  paraffin  oil,  or  solid 
sulphur,  occupied  the  intervening  space,  the  effect  pro- 
duced by  the  presence  of  the  electrified  body  at  the 
same  distance  would  have  beeri  greater.  The  power  of 
a  body  thus  to  allow  the  inductive  influence  of  an 
electrified  body  to  act  across  it  is  called  its  inductive 
capacity  (see  Article  49  and  Lesson  XXII.) 

22.  The  Electrophorus.-— We  are  now  prepared 
to  explain  the  operation  of  a  simple  and  ingenious 
instrument,  devised  by  Volta  in  1775,  for  the  purpose 
of  procuring,  by  the  principle  of  induction,  an  unlimited., 


CHAP.  I.]    ELECTRICITY  AND  MAGNETISM. 


number  of  charges  of  electricity  from  one  single  charge. 
This  instrument  is  the  Blectrophorus  (Fig.  12).  It 
consists  of  two  parts,  a  round  cake  of  resinous  material 
cast  in  a  metal  dish  or  "sole,"  about  12  inches  in 
diameter,  and  a  round  disc  of  slightly  smaller  diameter 
made  of  metal,  or  of  wood  covered  with  tinfoil,  and 


i'ig.  12 

provided  with  a  glass  handle.  Shellac,  or  sealing-wax, 
or  a  mixture  of  resin,  shellac,  and  Venice  turpentine,  may 
be  used  to  make  the  cake.  A  slab  of  sulphur  will 
also  answer,  but  it  is  liable  to  crack.  Sheets  of  hard 
ebonised  indiarubber  are  excellent ;  but  the  surface  of 
this  substance  requires  occasional  washing  with  ammonia 
and  rubbing  with  paraffin  oil,  as  the  sulphur  contained 


24  ELEMENTARY  LESSONS  ON      [CHAP.  i. 

in  it  is  liable  to  oxidise  and  to  attract  moisture.  To  use 
the  electrophorus  the  resinous  cake  must  be  beaten  or 
rubbed  with  a  warm  piece  of  woollen  cloth,  or,  better 
still,  with  a  cat's  skin.  The  disc  or  "  cover "  is  then 
placed  upon  the  cake,  touched  momentarily  with  the 
finger,  then  removed  by  taking  it  up  by  the  glass  handle, 
when  it  is  found  to  be  powerfully  electrified  with  a  posi- 
tive charge,  so  much  so  indeed  as  to  yield  a  spark  when 
the  knuckle  is  presented  to  it.  The  "  cover "  may  be 
replaced,  touched,  and  once  more  .removed,  and  will 
thus  yield  any  number  of  sparks,  the  original  charge  on 
the  resinous  plate  meanwhile  remaining  practically  as 
strong  as  before. 


-• A 


1 


Fig.  13.  Fig.  14. 

The  theory  ot  the  electrophorus  is  very  simple,  pro- 
vided the  student  has  clearly  grasped  the  principle  of 
induction  explained  above.  When  the  resinous  cake 
is  first  beaten  with  the  cat's  skin  its  surface  is  negatively 
electrified,  as  indicated  in  Fig.  13.  When  the  meta! 
disc  is  placed  down  upon  it,  it  rests  really  only  on  three 
or  four  points  of  the  surface,  and  may  be  regarded  as  an 
insulated  conductor  in  the  presence  of  an  electrified 
body.  The  negative  electrification  of  the  cake  therefore 
acts  inductively  on  the  metallic  disc  or  "  cover,"  attract- 
ing a  positive  charge  to  its  under  side,  and  repelling 
a  negative  charge  to  its  upper  surface.  This  state 
of  things  is  shown  in  Fig.  14.  If  now.  the  cover  be 
touched  for  an  instant  M'ith  the  finger,  the  negative 
charge  of  the  upper  surface  (which  is  upon  the  upper 


CHAP,  r.]    ELECTRICITY  AND  MAGNETISM.  ^  25 

surface  being  repelled  by  the  negative  charge  on  the  cake) 
will  be  neutralised  by  electricity  flowing  in  from  the 
earth  through  the  hand  and  body  of  the  experimenter. 
The  attracted  positive  charge  will,  however,  remain,  being 
bound  as  it  were  by  its  attraction  towards  the  negative 
charge  on  the  cake.  Fig.  15  shows  the  condition  of 
things  after  the  cover  has  been  touched.  If,  finally,  the 
cover  be  lifted  by  its  handle,  the  remaining  positive 
charge  will  be  no  longer  "  bound  "  on  the  lower  surface 
by  attraction,  but  will  distribute  itself  on  both  sides  of 


1 


Fig.  15.  Kig.  16. 

the  cover,  and  may  be  used  to  give  a  spark,  as  already 
said.  It  is  clear  that  no  part  of  the  original  charge  has 
been  consumed  in  the  process,  which  may  be  repeated 
as  often  as  desired.  As  a  matter  of  fact,  the  charge  on 
the  cake  slowly  dissipates — especially  if  the  air  be  damp. 
Hence  it  is  needful  sometimes  to  renew  the  original 
charge  by  afresh  beating  the  cake  with  the  cat's  skin. 
The  labour  of  touching  the  cover  with  the  finger  at  each 
operation  may  be  saved  by  having  a  pin  of  brass  or  a 
strip  of  tinfoil  projecting  from  the  metallic  "  sole  "  on  to 
the  top  of  the  cake,  so  that  it  touches  the  plate  each 
time,  and  thus  neutralises  the  negative  charge  by  allow- 
ing electricity  to  flow  in  from  the  earth. 

Since  the  electricity  thus  yielded  by  the  electrophorus 


26  ELEMENTARY  LESSONS  ON          [CHAP,  t 


is  not  obtained  at  the  expense  of  any  part  of  the  original 
charge,  it  is  a  matter  of  some  interest  to  inquire  what 
the  source  is  from  which  the  energy  of  this  apparently 
unlimited  supply  is  drawn ;  for  it  cannot  be  called 
into  existence  without  the  expenditure  of  some  other 
form  of  energy,  any  more  than  a  bteam-engine  can  work 
without  fuel.  As  a  matter  of  fact  it  is  found  that  it 
is  a  little  harder  work  to  lift  up  the  cover  when  it 
is  charged  with  the  +  electricity  than  if  it  were  not 
charged  ;  for,  when  charged,  there  is  the  force  of  the 
electric  attraction  to  be  overcome  as  well  as  the  force 
of  gravity.  Slightly  harder  work  is  done  at  the  ex- 
pense of  the  muscular  energies  of  the  operator  ;  and  this 
is  the  real  origin  of  the  eneigy  stored  up  in  the  separate 
charges. 

23.  Continuous   Elecfcrophori.  —  The  purely  me- 
chanical actions   of  putting   down   the   disc   on   to    the 
cake,  touching   it,  and  lifting  it  up,  can  be  performed 
automatically    by    suitable     mechanical    arrangements, 
which  render  the  production  of  these  inductive  charges 
practically  continuous.      The  earliest  of  such   contin- 
uous electropbori  was  Bennet's  "  Doubler,"  the  latest 
is  Wimshturst's  machine,  described  in  Lesson  V. 

24.  "Free"    and     "Bound"    Electricity.  —  We 
have  spoken  of  a  charge  of  electricity  on  the  surface  of 
a  conductor,  as  being  "  bound  "  when  it  is  attracted  by 
the  presence  of  a  neighbouring  charge  of  the  opposite 
kind.     The  converse  term  "  free  "  is  sometimes  applied 
to  the  ordinary  state  of  electricity  upon  a  charged  con- 
ductor, not  in  the  presence  of  a  charge  of  an  opposite 
kind.      A  "free"  charge  upon   an   insulated   conductoi 
flows  away  instantaneously  to  the  earth,  if  a  conducting 
channel  be   provided,  as  will   be   explained  in  the  next 
lesson.      It  is  immaterial  what  point  of  the  conductor  be 
touched.      Thus,   in    the   case  represented    in   Fig.   10, 
wherein  a  +  electrified  body  induces  —  electrification  at 
the  near  end,  and  4-  electrification  at  the  far  end  of  ar, 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM.  27 

* 

insulated  conductor,  the  —  charge  is  "  bound,"  being 
attracted,  while  the  +  charge  at  the  other  end,  being 
repelled,  is  "free";  and  if  the  insulated  conductor  be 
touched  by  a  person  standing  on  the  ground,  the  "free" 
electricity  will  flow  away  to  the  earth  through  his  body, 
while  the  "  bound "  electricity  will  remain,  no  matter 
whether  he  touch  the  conductor  at  the  far  end,  or  at  the 
near  end,  or  at  the  middle. 

25.  Inductive  method  of  charging  the  Gk>ld- 
leaf  Electroscope. — The  student  will  now  be  prepared 
to  understand  the  method  by  which  a  Gold-Leaf  Electro- 
scope can  be  charged  with  the  opposite  kind  of  charge  to 
that  of  the  electrified  body  used  to  charge  it.  In  Lesson 
II.  it  was  assumed  that  the  way  to  charge  an  electro- 
scope was  to  place  the  excited  body  in  contact  with  the 
knob,  and  thus  permit,  as  it  were,  a  small  portion  of  the 
charge  to  flow  into  the  gold  leaves.  A  rod  of  glass 
rubbed  on  silk  being  +  would  thus  obviously  impart  + 
electrification  to  the  gold  leaves. 

Suppose,  however,  the  rubbed  glass  rod  to  be  held  a 
few  inches  above  the  knob  of  the  electroscope,  as  is 
indeed  shown  in  Fig.  7.  Even  at  this  distance  the  gold 
leaves  diverge,  and  the  effect  is  due  to  induction.  The 
gold  leaves,  and  the  brass  wire  and  knob,  form  one  con- 
tinuous conductor,  insulated  from  the  ground  by  the 
glass  jar.  The  presence  of  the  +  electricity  of  the 
glass  acts  inductively  on  this  "  insulated  conductor," 
inducing  -  electrification  on  the  near  end  or  knob,  and 
inducing  +  at  the  far  end,  /'.<?.,  on  the  gold  leaves, 
which  diverge.  Of  these  two  induced  charges,  the  - 
on  the  knob  is  "  bound,"  while  the  +  on  the  leaves  is 
"  free."  If  now,  while  the  excited  rod  is  still  held  above 
the  electroscope,  the  knob  be  touched  by  a  person 
standing  on  the  ground,  one  of  these  two  induced  charges 
flows  to  the  ground,  namely  the  free  charge— not  that 
on  the  knob  itself,  for  it  was  "  bound,"  but  that  on  the 
gold  leaves  which  was  "  free " — and  the  gold  leaves 


28  ELEMENTARY  LESSONS  ON        [CHAP,  i 

instantly  drop  down  straight.  There  now  remains  only 
the  —  charge  on  the  knob,  "  bound "  so  long  as  the 
+  charge  of  the  glass  rod  is  near  to  attract  it.  But 
if,  finally,  the  glass  rod  be  taken  right  away,  the  - 
charge  is  no  longer  "  bound "  on  the  knob,  but  is 
"  free  "  to  flow  into  the  leaves,  which  once  more  diverge 
— but  this  time  with  a  negative  electrification. 

26.  "  The  Return-Shock." — It  is  sometimes  noticed 
that,  when  a  charged  conductor  is  suddenly  discharged, 
a  discharge  is  felt  by  persons  standing  near,  or  may 
even  affect  electroscopes,  or  yield  sparks.  This  action, 
known  as  the  "  return-shock,"  is  due  to  induction.  For 
in  the  presence  of  a  charged  conductor  a  charge  of 
opposite  sign  will  be  induced  in  neighbouring  bodies, 
and  on  the  discharge  of  the  conductor  these  neighbour- 
ing bodies  may  also  suddenly  discharge  their  induced 
charge  into  the  earth,  or  into  other  conducting  bodies. 
A  "  return-shock  "  is  sometimes  felt  by  persons  standing 
on  the  ground  at  the  moment  when  a  flash  of  lightning 
has  struck  an  object  some  distance  away. 


LKSSON  IV. —  Conduction  and  Distribution  of  Electricity. 

27.  Conduction. — Toward  the  close  of  Lesson  I. 
we  explained  how  certain  bodies,  such  as  the  metals, 
conduct  electricity,  while  others  are  non-conductors  or 
insulators.  This  discovery  is  due  to  Stephen  Gray ; 
who,  in  1729,  found  that  a  cork,  inserted  into  the  end 
of  a  rubbed  glass  tube,  and  even  a  rod  of  wood  stuck 
into  the  cork,  possessed  the  power  of  attracting  light 
bodies  He  found,  similarly,  that  metallic  wire  and  pack- 
thread conducted  electricity,  while  silk  did  not. 

We  may  repeat  these  experiments  by  taking  (as  in 
Fig.  17)  a  glass  rod,  fitted  with  a  cork  and  a  piece  of 
wood.  If  a  bullet  or  a  brass  knob  be  hung  to  the  end  of 
this  by  a  linen  thread  or  a  v.ire,  it  is  found  that  when  the 


CHAP.  I.]    ELECTRICITY  AND  MAGNETISM.  29 

glass  tube  is  rubbed  the  bullet  acquires  the  property  of 
attracting  light  bodies.  If  a  dry  silk  thread  fs  used, 
however,  no  electricity  will  flow  down  to  the  bullet. 

Gray  even  succeeded  in  transmitting  a  charge  of 
electricity  through  a  hempen  thread  over  700  feet  long, 
suspended  on  silken  loops.  A  little  later  Du  Fay 
succeeded  in  sending  electricity  to  no  less  a  distance 
than  1256  feet  through  a  moistened  thread,  thus  proving 
the  conducting  power  of  moisture  From  that  time  the 
classification  of  bodies  into  conductors  and  insulators 
has  been  observed. 


Fig.  17 

This  distinction  cannot,  however,  be  entirely  main- 
tained, as  a  large  class  of  substances  occupy-  an  inter- 
mediate ground  as  partial  conductors.  For  example,  dry 
wood  is  a  bad  conductor  and  also  a  bad  insulator;  it 
is  a  good  enough  conductor  to  conduct  away  the  high- 
potential  electricity  obtained  by  friction  ;  but  it  is  a 
bad  conductor  for  the  relatively  low-potential  electricity 
iof  small  voltaic  batteries.  Substances  that  are  very  bad 
[conductors  are  said  to  offer  a  great  resistance  to  the 


30 


ELEMENTARY  LESSONS  ON        [CHAP*  I 


Good  Conductors. 


Partial  Conductors. 


flow  of  electricity  through  them.  There  is  indeed  no 
substance  so  good  a  conductor  as  to  be  devoid  of  resist- 
ance. There  is  no  substance  of  so  high  a  resistance  as 
not  to  conduct  a  little.  Even  silver,  which  conducts  best 
of  all  known  substances,  resists  the  flow  of  electricity  to 
a  small  extent ;  and,  on  the  other  hand,  such  a  non-con- 
ducting substance  as  glass,  though  its  resistance  is  many 
million  times  greater  than  any  metal,  does  allow  a  very 
small  quantity  of  electricity  to  pass  through  it.  In  the 
following  list,  the  substances  named  are  placed  in  order, 
each  conducting  better  than  those  lower  down  on  the  list 

Silver  . 
Copper  . 
Other  metals 
Charcoal . 
Water  . 
The  body 
Cotton  . 
Dry  Wood 
Marble  . 
Paper  . 
Oils 

Porcelain 
Wool      . 
Silk 
Resin 

Guttapercha 
Shellac  . 
Ebonite  . 
Paraffin  .- 
Glass  ^  . 
Dry  air  . 

A  simple  way  of  observing  experimentally  whether  a 
body  is  a  conductor  or  not,  is  to  take  a  charged  gold- 
leaf  electroscope,  and,  holding  the  substance  to  be 
examined  in  the  hand,  touch  the  knob  of  the  electro- 
scope with  it.  If  the  substance  is  a  conductor  the 
electricity  will  flow  away  through  it  arid  through  the 
body  to  the  earth,  and  the  electroscope  will  be  discharged. 
Through  good  conductors  the  rapidity  of  the  flow  is  so 


Non-Conductors  or 
Insulators. 


CHAP.  i.J    ELECTRICITY  AND  MAGNETISM.  31 


great  that  the  discharge  is  practically  instantaneous. 
Further  information  on  this  Question  is  given  in  Lesson 
XXIII. 

28.  Distribution  of  Electricity  on  Bodies. — It 
electricity  is  produced  at  one  part  of  a.  non-conducting 
body,  it  remains  at  that  point  and   does  not  /low  over 
the  surface,  or  at  most  flows  over  it  excessively  slowly. 
Thus  if  a  glass  tube  is  rubbed  at  one  end,  only  that  one 
end  is  electrified.      If  a  warm  cake  of  resin  be  rubbed  at 
one  part  with  a  piece  of  cloth,  only  the  portion  nibbed 
will  attract  light  bodies.      The  case  is,  however,  wholly 
different  when  a  charge  of  electricity  is  hnpaited  to  any 
part    of  a    conducting    body    placed    on    an    insulating 
support,   for  it  instantly  distributes  itself  all   over   the 
surface,  though  in  general  not  uniformly  over  all  points 
of  the  surface. 

29.  The    Charge   resides    on  the   surface. — A 
charge   of   electricity    resides    only    on    the    surface    of 
conducting  bodies.     This  is  proved  by  the  fact  that  it 
is  found  to  be  immaterial  to  the  distribution  what  the 
interior  of  a  conductor  is  made  of;  it  maybe  solid  metal, 
or  hollow,  or  even  consist  of  wood  covered  with  tinfoil 
or  gilt,  but,  if  the  shape  be  the  same,  the  charge  will 
distribute  itself  precisely  in  the  same  manner  over  the 
surface.     There    are   also   several   ways   of  proving  by 
direct  experiment  this  very  important  fact.     Let  a  hollow 
metal  ball,  having  an  aperture  at  the  top,  be  taken  (as  in 
Fig.  1 8),  and  set  upon  an  insulating  stem,  and  charged 
by  sending  into  it  a  few  sparks  from  an  electrophorus. 
The  absence  of  any  charge  in  the  interior  may  be  shown 
as   follows  : — In   order   to   observe   the   nature    of  the 
electricity  of  a  charged  body,  it  is  convenient  to  have 
some  means  of  removing  a  small  quantity  of  the  charge 
as  a  sample  for  examination.      To  obtain  such  a  sample 
a  little  instrument  known  as  a  proof-plane  is  employed 
It  consists  of  a  little  disc  of  sheet  copper  or  of  gilt  papei 
fixed  at  the  end  of  a  small  glass  rod.     If  this  disc  is  laid 


ELEMENTARY  LESSONS  ON         [CHAT    i. 


on  the  surface  of  an  electrified  body  at  any  point,  par? 
of  the  electricity  flows  into  it,  and  it  may  be  then  re- 
moved, and  the  sample  thus  obtained  may  be  examined 
with  a  Gold-leaf  Electroscope  in  the  ordinary  way.  For 
some  purposes  a  metallic  bead,  fastened  to  the  end  of  a 
glass  rod,  is  more  convenient  than  a  flat  disc.  If  such 


Fig.  1 8. 

a  proof-plane  be  applied  to  the  outside  of  our  electrified 
hollow  ball,  and  then  touched  on  the  knob  of  an  electro- 
scope, the  gold  leaves  will  diverge,  showing  the  presence 
of  a  charge.  But  if  the  proof-plane  be  carefully  inserted 
through  the  opening,  and  touched  against  the  inside  of 


CHAP,  i.j    ELECTRICITY  AND  MAGNETISM. 


33 


the  globe  and  then  withdrawn,  it  will  be  found  that  the 
inside  is  destitute  of  electricity.  An  electrified  pewter 
mug  will  show  a  similar  result,  and  so  will  even  a 
cylinder  of  gauze  wire. 

3O.  Blot's  experiment. — Biot  proved  the  same  fact 
in  another  way.  A  copper  ball  was  electrified  and 
insulated.  Two  hollow  hemispheres  of  copper,  of  a 
larger  size,  and  furnished  with  glass  handles,  were  then 
placed  together  outside  it  (Fig.  19).  So  long  as  they 
did  not  come  into  contact  the  charge  remained  on  the 


A 


Fig.  19. 

inner  sphere  ;  but  if  the  outer  shell  touched  the  inner 
sphere  for  but  an  instant,  the  whole  of  the  electricity 
passed  to  the  exterior ;  and  when  the  hemispheres  were 
separated  and  removed  the  inner  globe  was  found  to  be 
completely  discharged. 

31.  Further  explanation. — Doubtless  the  explana- 
tion of  this  behaviour  of  electricity  is  to  be  found  in 
the  property  previously  noticed  as  possessed  by  either 
kind  of  electricity,  namely,  that  of  repelling  itself;  hence 
it  retreats  as  far  as  can  be  from  the  centre  and  remains 


34  ELEMENTARY  LESSONS  ON         [CHAP.  I, 

upon  the  surface.  An  important  proposition  concerning 
the  absence  of  electric  force  within  a  closed  conductor  is 
proved  in  Lesson  XX.  ,  meanwhile  it  must  be  noted  that 
the  proofs,  so  far,  are  directed  to  demonstrate  the 
absence  of  a  free  charge  of  electricity  in  the  interior 
of  hollow  conductors.  Many  other  experiments  have 
been  devised  in  proof.  Thus,  Terquem  showed  that 
a  pair  of  gold  leaves  hung  inside  a  wire  cage  could 
not  be  made  to  diverge  when  the  cage  was  elec- 
trified. Faraday  constructed  a  conical  bag  of  linen- 


Fig.  20. 

gauze,  supported  as  in  Fig.  20,  upon  an  insulating 
stand,  and  to  which  silk  strings  were  attached,  by  which 
it  could  be  turned  inside  out.  It  was  charged,  and 
the  charge  was  shown  by  the  proof -plane  and  electro- 
scope to  be  on  the  outside  of  the  bag.  On  turning  it 
inside  out  the  electricity  was  once  more  found  outside. 
Faraday's  most  striking  experiment  was  made  with  a 
hollow  cube,  measuring  12  feet  each  way,  built  of  wood, 
covered  with  tinfoil,  insulated,  and  charged  with  a 
powerful  machine,  so  that  large  sparks  and  brushes 


CHAP.  i.j        ELECTRICITY  AND  MAGNETISE  35 

were  darting  off  from  every  part  of  its  outer  surface. 
Into  this  cube  Faraday  took  his  most  delicate  electro- 
scopes ;  but  once  within  he  failed  to  detect  the  least 
influence  upon  them. 

32.  Applications. — Advantage  is  taken  of  this  in 
the   construction   of  delicate    electrometers    and    other 
instruments,    which    can  be    effectually    screened   from 
the  influence  of  electrified  bodies    by   enclosing   them 
in  a  thin  metal  cover,  closed   all  round,  except  where 
apertures  must  be  made  for  purposes  of  observation.     It 
has  also  been  proposed  by  the  late  Prof.  Clerk  Maxwell 
to  protect  buildings  from  lightning  by  covering  them 
on  the  exterior  with  a  network  of  wires. 

33.  Apparent  Exceptions. — There    are  two  ap- 
parent exceptions  to  the  law  that  electricity  resides  only 
on  the  outside  of  conductors.     ( I )  If  there  are  electrified 
insulated  bodies  actually  placed  inside  the  hollow  con- 
ductor, the  presence  of  these  electrified  bodies  acts  in- 
ductively and  attracts  the  opposite  kind  of  electricity  to 
the   inner  side    of  the   hollow  conductor.      (2)  When 
electricity  flows  in  a  current,  it  flows  through  the  sub- 
stance of  the  conductor.     The  law  is  limited  therefore 
to  electricity  at  rest, — that  is,  to  statical  charges. 

34.  Faraday's  "  Ice-pail "  Experiment. — One  ex- 
periment  of  Faraday  deserves  notice,  as  showing  the 
part    played    by  induction    in   these  phenomena.      He 
gradually  lowered  a  charged  metallic  ball  into  a  hollow 
conductor  connected   by  a  wire  to  a  gold-leaf  electro- 
scope (Fig.  21),  and  watched  the  effect.     A  pewter  ice- 
pail  being  convenient  for  his  purpose,  this  experiment  is 
continually  referred  to  by  this  name,  though  any  other 
hollow  conductor — a  tin  canister  or  a  silver  mug,  placed 
on   a  glass   support — would   of  course  answer  equally 
well.      The   following   effects   are  observed  : —  Suppose 
the  ball  to  have  a  +  charge :  as  it  is  lowered  into  the 
hollow  conductor  the  gold  leaves  begin  to  diverge,  for 
the  presence  of  the  charge  acts  inductively,  and  attracts 


ELEMENTARY  LESSONS  ON         [CHAP.  i. 


a  *-  charge  into  the  interior  and  repels  a  +  charge  to  the 
exterior.  The  gold  leaves  diverge  more  and  more  until 
the  ball  is  right  within  the  hollow  conductor,  after  which 
no  greater  divergence  is  obtained.  On  letting  the  ball 
touch  the  inside  the  gold  leaves  still  remain  diverging 
as  before,  and  if  now  the  ball  is  pulled  out  it  is  found 
to  have  lost  all  its  electricity.  The  fact  that  the  gold 

leaves  diverge  no  wider 
after  the  ball  touched 
than  they  did  just 
before,  proves  that 
when  the  charged  ball 
is  right  inside  the 
hollow  conductor  the 
induced  charges  are 
each  of  them  precisely 
equal  in  amount  to 
its  own  charge,  and  the 
interior  negative  charge 
exactly  neutralises  the 
charge  on  the  ball  at 


the  moment  when  they 
touch,  leaving  the  equal 
exterior  charge  un- 
changed. An  electric 

cage,  such  as  this  ice-pail,  when  connected  with  an 
electroscope  or  electrometer,  affords  an  excellent  means 
of  examining  the  charge  on  a  body  small  enough  to  be 
hung  inside  it.  For  without  using  up  any  of  the  charge 
of  the  body  (which  we  are  obliged  to  do  when  applying 
the  method  of  the  proof-plane)  we  can  examine  tho 
induced  charge  repelled  to  the  outside  of  the  cage, 
which  is  equal  in  amount  and  of  the  same  sign. 

35.  Distribution  of  Charge. — A.  charge  of  elec- 
tricity is  not  usually  distributed  uniformly  over  the 
surfaces  of  bodies.  Experiment  shows  that  there  is 
more  electricity  on  the  edges  and  corners  of  bodies  than 


CHAP,  i.]     ELECTRICITY  AND  MAGNETISM.  37 

upon  their  flatter  parts.  This  distribution  can  be  de- 
duced from  the  theory  laid  down  in  Lesson  XX.,  but 
meantime  we  will  give  some  of  the  chref  cases  as  they 
can  be  shown  to  exist.  The  term  Electric  Density  is 
used  to  signify  the  amount  of  electricity  at  any  point  of 
a  surface  ;  the  electric  density  at  a  point  is  the  member 
of  units  of  electricity  per  unit  of  area  (i.e.  per  square 
inch,  or  per-^square  centimetre),  the  distribution  being 
supposed  uniform  over  this  small  surface. 

(a)  Sphere. — The  distribution  of  a  charge  over  an 
insulated  sphere  of  conducting  material  is  uniform, 
provided  the  sphere  is  remote  from  the  presence  of  all 
other  conductors  and  all  other  electrified  bodies  ;  or,  in 


Fig.  22. 

other  words,  the  density  is  uniform  all  over  it.  This  is 
symbolised  by  the  dotted  line  round  the  sphfcre  in  Fig. 
22,  a,  which  is  at  an  equal  .distance  from  the  sphere  all 
round,  suggesting  an  equal  thickness  of  electricity  at 
every  point  of  the  surface.  It  must  be  remembered 
that  the  charge  is  not  really  of  any  perceptible  thickness 
at  all ;  it  resides  on  or  at  the  surface,  but  cannot  be 
said  to  form  a  stratum  upon  it. 

(b)  Cylinder  -with  rounded  ends.  —  Upon  an 
elongated  conductor,  such  as  is  frequently  employed  in 
electrical  apparatus,  the  density  is  greatest  at  the  ends 
where  the  curvature  of  the  surface  is  the  greatest. 


j8  ELEMENTARY  LESSONS  ON         [CHAT.  i. 


(o)  Two  Spheres  in  contact. — Tf  two  spheres  in 
contact  with  each  other  are  insulated  and  charged,  it  is 
found  that  the  density  is  greatest  at  the  parts  farthest 
from  the  point  of  contact,  and  least  in  the  crevice 
between  them.  If  the  spheres  are  of  unequal  sizes 
the  density  is  greater  on  the  smaller  sphere,  which  has 
the  surface  more  curved.  On  an  egg-shaped  or  pear- 
shaped  conductor  the  density  is  greatest  at  the  small 
end.  On  a  cone  the  density  is  greatest  at  the  apex  ; 
and  if  the  cone  terminnte  in  a  sharp  point  the  density 
there  is  very  much  greater  than  at  any  other  point.  At 
a  point,  indeed,  the  density  of  tLe  collected  electricity 
may  be  so  great  as  to  electrify  the  neighbouring  particles 
of  air,  which  then  are  repelled,  thus  producing  a  con- 
tinual loss  of  charge.  For  this  reason  points  and  sharp 
edges,  are  always  avoided  on  electrical  apparatus,  except 
where  it  is  specially  desired  to  set  up  a  discharge. 

(d)  Flat  Disc. — The  density  of  a  charge  upon  a 
flat  disc  is  greater,  as  we  should  expect,  at  the  edges 
than  on  the  flat  surfaces ;  but  over  the  flat  surfaces  the 
distribution  is  fairly  uniform. 

These  various  facts  are  ascertained  by  applying  a 
small  proof- plane  successively  at  various  points  of  the 
electrified  bodies  and  examining  the  amount  taken  up  by 
the  proof-plane  by  means  of  an  electroscope  or  electro- 
meter. Coulomb,  who  investigated  mathematically  ar- 
well  as  experimentally  many  of  the  important  cases  of 
distribution,  employed  the  torsion  balance  to  verify  his 
calculations.  He  investigated  thus  the  case  of  the 
ellipsoid  of  revolution,  and  found  the  densities  of  the 
charges  at  the  extremities  of  the  axis  to  be  pioportional 
to  the  lengths  of  those  axes.  He  also  showed  that  the 
density  of  the  charge  at  any  other  point  of  the  surface  of 
the  ellipsoid  was  proportional  to  the  length  of  the  per- 
pendicular drawn  from  the  centre  to  the  tangent  at  that 
point.  Riess  also  investigated  several  interceding  cr,se3 
of  distribution.  He  found  the  density  at  the  middle  of 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM.  39 

the  edges  of  a  cube  to  be  nearly  two  and  a  half  times 
as  great  as  the  density  at  the  middle  of  a  face  ;  while 
the  density  at  a  corner  of  the  cube  was  more  than  four 
times  as  great. 

36.  Redistribution  of  Charge. —  If  any  portion 
of  the  charge  of  an  insulated  conductor  be  removed,  the 
remainder  of  the   charge  will   immediately  redistribute 
itself  over  the  surface  in  the  same  manner  as  the  original 
charge,  provided  it  be  also  isolated,  i.e.,  that  no  other 
conductors   or  charged  bodies   be  near  to  perturb  the 
distribution  by  complicated  effects  of  induction. 

If  a  conductor  be  charged  with  any  quantity  of  elec- 
tricity, and  another  conductor  of  the  same  size  and  shape 
(but  uncharged)  be  brought  into  contact  with  it  for  an 
instant  and  then  separated,  it  will  be  found  that  the 
change  has  divided  itself  equally  between  them.  In  the 
same  way  a  charge  may  be  divided  equally  into  three  or 
more  parts  by  being  distributed  simultaneously  over  three 
or  more  equal  and  similar  conductors  brought  into  contact. 

If  two  equal  metal  balls,  suspended  by  silk  strings, 
charged  with  unequal  quantities  of  electricity,  are 
brought  for  an  instant  into  contact  and  then  separated, 
it  will  be  found  that  the  charge  has  redistributed  itsel/ 
fairly,  half  the  sum  of  the  two  charges  being  now  the 
charge  of  each.  This  may  even  be  extended  to  the 
case  of  charges  of  opposite  signs.  Thus,  suppose  two 
similar  conductors  to  be  electrified,  one  with  a  positive 
charge  of  5  units  and  the  other  with  3  units  of  negative 
charge,  when  these  are  made  to  touch  and  separated, 
each  will  have  a  positive  charge  of  T  unit ;  for  the 
algebraic  sum  of  +  5  and  —  3  is  +  2,  which,  shared 
between  the  two  equal  conductors,  leaves  +  i  for  each. 

37.  Capacity  of  Conductors. — If  the  conductors 
be  unequal  in  size,  or  unlike  in  form,  the  shares  taken 
by  each   in   this   redistribution   will   not  be   equal,  but 
will   be  proportional   to   the    electric   capacities   of  the 
conductors.     The  definition  of  capacity  in  its  relation 


40  ELEMENTARY  LESSONS  ON         [CHAP,  i 

to  electric  quantities  is  given  in  Lesson  XX.,  Art.  246. 
We  may,  however,  make  the  remark,  that  two  insulated 
conductors  of  the  same  form,  but  of  different  sizes,  differ 
in  their  electrical  capacity;  for  the  larger  one  must 
have  a  larger  amount  of  electricity  imparted  to  it  in 
order  to  electrify  its  surface  to  the  same  degree.  The 
term  potential  is  employed  in  this  connection,  in  the 
following  way : — A  given  quantity  of  electricity  will 
electrify  an  isolated  body  up  to  a  certain  "  potential " 
(or  power  of  doing  electric  work)  depending  on  its 
capacity.  A  large  quantity  of  electricity  imparted  to  a 
conductor  of  small  capacity  will  electrify  it  up  to  a 
very  high  potential;  just  as  a  large  quantity  of  water 
poured  into  a  vessel  of  narrow  capacity  will  raise  the 
surface  of  the  water  to  a  high  level  in  the  vessel.  The 
exact  definition  of  Potential,  in  terms  of  energy  spen* 
against  the  electrical  forces,  is  given  in  the  Lesson  on 
Electrostatics  (Art.  237). 

It  will  be  found  convenient  to  refer  to  a  positively 
electrified  body  as  one  electrified  to  a  positive  or  high 
potential;  while  a  negatively  electrified  body  may  be 
looked  upon  as  one  electrified  to  a  low  or  negative 
potential.  And  just  as  we  take  the  level  of  the  sea 
as  a  zero  level,  and  measure  the  heights  of  mountains 
above  it,  and  the  depths  of  mines  below  it,  using  the 
sea  level  as  a  convenient  point  of  reference  for  differ- 
ences of  level,  so  we  lake  the  potential  of  the  earth's 
surface  (for  the  surface  of  the  earth  is  always  electrified 
to  a  certain  degree)  as  zero  potential,  and  use  it  a?  a 
convenient  point  of  reference  from  which  to  measure 
differences  of  electric  potential. 

LESSON  V. — Electrical  Machines. 

38.  For  the  purpose  of  procuring  larger  supplies  ol 
electricity  than  can  be  obtained  by  the  rubbing  of  a  rod 
of  glass  or  shellac,  electrical  machines  have  beer 


CHAP.  i.J    ELECTRICITY  AND  MAGNETISM.  41 

devised.  All  electrical  machines  consist  of  two  parts, 
one  for  producing,  the  other  for  collecting,  the  electricity. 
Experience  has  shown  that  the  quantities  of  +  and  — 
electrification  developed  by  friction  upon  the  two  surfaces 
rubbed  against  one  another  depend  on  the  amount  of 
friction,  upon  the  extent  of  the  surfaces  rubbed,  and  also 
upon  the  nature  of  the  substances  used.  If  the  two 
substances  employed  are  near  together  on  the  list  of 
electrics  given  in  Art.  5,  the  electrical  effect  of  rubbing 
them  together  will  not  be  so  great  as  if  two  substances 
widely  separated  in  the  series  are  chosen.  To  obtain 
the  highest  effect,  the  most  positive  and  the  most 
negative  of  the  substances  convenient  for  the  construc- 
tion of  a  machine  should  be  taken,  and  the  greatest 
available  surface  of  them  should  be  subjected  to  friction, 
the  moving  parts  having  a  sufficient  pressure  against  one 
another  compatible  with  the  required  velocity. 

The  earliest  form  of  electrical  machine  was  devised 
by  Otto  von  Guericke  of  Magdeburg,  and  consisted  of 
a  globe  of  sulphur  fixed  upon  a  spindle,  and  pressed 
with  the  dry  surface  of  the  hands  while  being  made  to 
rotate  ;  with  this  he  discovered  the  existence  of  electric 
sparks  and  the  repulsion  of  similarly  electrified  bodies. 
Sir  Isaac  Newton  replaced  Von  Guericke's  globe  of 
sulphur  by  a  globe  of  glass.  A  little  later  the  form  of 
the  machine  was  improved  by  various  German  electri- 
cians ;  Von  Bose  added  a  collector  or  "  prime  con- 
ductor," in  the  shape  of  an  iron  tube,  supported  by  a 
person  standing  on  cakes  of  resin  to  insulate  him,  or 
suspended  by  silken  strings  ;  Winckler  of  Leipzig  sub- 
stituted a  leathern  cushion  for  the  hand  as  a  rubber ; 
and  Gordon  of  Erfurth  rendered  the  machine  more  easy 
of  construction  by  using  a  glass  cylinder  instead  of  a 
glass  globe.  The  electricity  uas  led  from  the  excited 
cylinder  or  globe  to  the  prime  conductor  by  a  metallic 
chain  which  hung  over  against  the  globe.  A  pointed 
°ollecior  was  not  employed  until  after  Franklin's  famous 


42  ELEMENTARY  LESSONS  ON         [CHAP.  i. 

researches  on  the  action  of  points.  About  1760  De 
la  Fond,  Planta,  Ramsden.  and  Cuthbertson,  constructed 
machines  having  glass  plates  instead  of  cylinders.  The 
only  important  modifications  introduced  since  their  time 
are  the  substitution  of  ebonite  for  glass,  and  the  inven- 
tion of  machines  depending  on  the  principles  of  induc- 
tion and  convection. 

39.  The  Cylinder  Electrical  Machine. — The 
Cylinder  Electrical  Machine,  as  usually  constructed, 
consists  of  a  glass  cylinder  mounted  on  a  horizontal  axis 
capable  of  being  turned  by  a  handle.  Against  it  is 
pressed  from  behind  a  cushion  of  leather  stuffed  with 
horsehair,  the  surface  of  which  is  covered  with  a 
powdered  amalgam  of  zinc  or  tin.  A  flap  of  silk  attached 
to  the  cushion  passes  over  the  cylinder,  covering  its 


upper  half.  In  front  of  the  cylinder  stands  the  "prime 
conductor,"  which  is  made  of  meral,  and  usually  of  the 
form  of  an  elongated  cylinder  with  hemispherical  ends, 
mounted  upon  a  glass  stand.  At  the  end  of  the  prime 
conductor  nearest  the  cylinder  is  fixed  a  rod  bearing  a 
row  of  fine  metallic  spikes,  resembling  in  form  a  rake ; 
the  other  end  usually  carries  a  rod  terminated  in  a  brass 


CHAP.  i.J    ELECTRICITY  AND  MAGNETISM.  43 

ball  or  knob.  The  general  aspect  of  the  machine  is 
shown  in  Fig.  23.  When  the  handle  is  turned  the 
friction  between  the  glass  and  the  amalgam -coated 
surface  of  the  rubber  produces  a  copious  electrical 
action,  electricity  appearing  as  a  +  charge  on  the  glass, 
leaving  the  rubber  with  a  —  charge.  The  prime  con- 
ductor collects  this  charge  by  the  following  process : — 
The  +  charge  being  carried  round  on  the  glass  acts 
inductively  on  the  long  insulated  conductor,  repelling  a 
+  charge  to  the  far  end  ;  leaving  the  nearer  end  —  ly 
charged.  The  effect  of  the  row  of  points  is  to  drive  off 
in  a  continuous  discharge  -  ly  electrified  air  towards  the 
attracting  -{-  charge  upon  the  glass,  which  is  neutralised 
thereby ;  the  glass  thus  arriving  at  the  rubber  in  a 
neutral  condition  ready  to  be  again  excited.  This  action 
of  the  points  is  sometimes  described,  though  less  cor- 
rectly, by  saying  that  the  points  collect  the  +  electricity! 
from  the  glass.  If  it  is  desired  to  collect  also  the  — 
charge  of  the  rubber,  the  cushion  must  be  supported  on 
an  insulating  stem  and  provided  at  "the  back  with  a 
metallic  knob.  This  device,  permitting  either  kind  of 
charge  to  be  used  at  will,  is  due  to  Nairne.  It  is,  how- 
ever, more  usual  to  use  only  the  +  charge,  and  to 
connect  the  rubber  by  a  chain  to  "  earth,"  so  allowing 
the  —  charge  to  be  neutralised. 

4O.  The  Plate  Electrical  Machine. — The  Plate 
Machine,  as  its  name  implies,  is  constructed  with  a 
circular  plate  of  glass  or  of  ebonite,  and  is  usually  pro- 
vided with  two  pairs  of  rubbers  formed  of  double 
cushions,  pressing  the  plate  between  them,  placed  at  its 
highest  and  lowest  point,  and  provided  with  silk  flaps, 
each  extending  over  a  quadrant  of  the  circle.  The  prime 
conductor  is  either  double  or  curved  round  to  meet  the 
plate  at  the  two  ends  of  its  horizontal  diameter,  and  is 
furnished  with  two  sets  of  spikes,  for  the  same  purpose 
as  the  row  of  points  in  the  cylinder  machine.  A 
common  form  of  plate  machine  is  shown  in  Fig.  24. 


44 


ELEMENTARY  LESSONS  ON         [CHAP.  i. 


The  action  of  the  machine  is,  in  all  points  of  theoretical 
interest,  the  same  as  that  of  the  cylinder  machine.  Its 
advantages  are  that  a  large  glass  plate  is  more  easy  to 
construct  than  a  large  glass  cylinder  of  perfect  form,  and 
that  the  length  along  the  surface  of  the  glass  between  the 
collecting  row  of  points  and  the  edge  of  the  rubber 

cushions  is  greater 
in  the  plate  than  in 
the  cylinder  for  the 
same  amount  of  sur- 
face exposed  to  fric- 
tion ;  for,  be  it  re- 
marked, when  the 
two  electricities  thus 
separated  have  col- 
lected to  a  certain 
extent,  a  discharge 
will  take  place  along 
this  surface,  the 
length  of  which  limits 
therefore  the  power 
of  the  machine.  In 
a  more  modern  form, 


Fig.  24, 


due  to  Le  Roy,  and  modified  by  Winter,  there  is  but  one 
rubber  and  flap,  occupying  a  little  over  a  quadrant  of  the 
plate,  and  one  collector  or  double  row  of  points.  In 
Winter's  machine  the  prime  conductor  consists  of  a  ring- 
shaped  body,  for  which  the  advantage  is  claimed  of 
collecting  larger  quantities  of  electricity  than  the  more 
usual  sausage -shaped  conductor.  Whatever  advantage 
the  form  may  have  is  probably  due  to  the  curvature  of 
its  surface  being  on  the  whole  greater  than  that  of  the 
commoner  form. 

41.  Electrical  Amalgam. —  Canton,  finding  glass 
to  be  highly  electrified  when  dipped  into  dry  mercury, 
suggested  the  employment  of  an  amalgam  of  tin  with 
mercury  as  a  suitable  substance  wherewith  to  cover  the 


CHAP,  i.]     ELECTRICITY  AND  MAGNETISM.  45 

surface  of  the  rubbers.  An  amalgam  of  zinc  is  also 
effective  ;  though  still  better  is  Kienmayer's  amalgam, 
consisting  of  equal  parts  of  tin  and  zinc,  mixed  while 
molten  with  twice  their  weight  of  mercury.  Bisulphide 
of  tin  ("  mosaic  gold ")  may  also  be  used.  These 
amalgams  are  applied  to  the  cushions  with  a  little  stiff 
grease.  They  serve  the  double  purpose  of  conducting 
away  the  negative  charge  separated  upon  the  rubber 
during  the  action  of  the  machine,  and  of  affording  as  a 
rubber  a  substance  which  is  more  powerfully  negative 
(see  list  in  Art.  5)  than  the  leather  or  the  silk  of  the 
cushion  itself.  Powdered  graphite  is  also  good. 

42.  Precautions  in  using  Electrical  Machines. 
— Several  precautions  must  be  observed  in  the  use  of 
electrical  machines.  Damp  and  dust  must  be  scrupu- 
lously avoided.  The  surface  of  glass  is  hygroscopic, 
hence,  except  in  the  driest  climates,  it  is  necessary  to 
warm  the  glass  surfaces  and  rubbers  to  dissipate  the 
film  of  moisture  which  collects.  Glass  stems  for  in- 
sulation may  be  varniohed  with  a  thin  coat  of  shellac 
varnish,  or  with  paraffin  (solid).  A  few  drops  of 
anhydrous  paraffin  (obtained  by  dropping  a  lump  of 
sodium  into  a  bottle  of  paraffin  oil),  applied  with  a  bit  of 
flannel  to  the  previously  warmed  surfaces,  hinders  the 
deposit  of  moisture.  An  electrical  machine  which  has 
not  been  used  for  some  months  will  require  a  fresh  coat 
of  amalgam  on  its  rubbers.  These  should  be  cleaned 
and  warmed,  a  thin  uniform  layer  of  tallow  or  other  stiff 
grease  is  spread  upon  them,  and  the  amalgam,  previously 
reduced  to  a  fine  powder,  is  sifted  over  the  surface. 

All  points  should  be  avoided  in  apparatus  for 
fractional  electricity  except  where  they  are  desired,  like 
the  "  collecting  "  spikes  on  the  prime  conductor,  to  let  off 
a  charge  of  electricity.  All  the  rods,  etc.,  in  frictional 
apparatus  are  therefore  made  with  knobs,  so  as  to  avoid 
sharp  edges  and  points. 
43.  Experiments  with  the  Electrical  Machine. 


46 


ELEMENTARY  LESSONS  ON         [CHAP.  I. 


— With  the  abundant  supply  of  electricity  afforded  by 
the  electrical  machine,  many  pleasing  and  instructive 
experiments  are  possible.  The  phenomena  of  attrac- 
tion and  repulsion  can  be 
shown  upon  a  large  scale. 
Fig.  25  represents  a  device 
known  as  the  electric 
chimes,1  in  which  two  small 
brass  balls  hung  by  silk  strings 
are  set  in  motion  and  strike 
against  the  bells  between 
which  they  are  hung.  The 
two  outer  bells  are  hung  by 
metallic  wires  or  chains  to 
the  knob  of  the  machine. 
The  third  bell  is  hung  by  a 
silk  thread,  but  communi- 
cates with  the  ground  by  a 
brass  chain.  The  balls  are 


Fig.  25. 


first  attracted  to  the  electrified  outer  bells,  then  repelled, 
and,  having  discharged  themselves  against  the  uninsul- 
ated central  bell,  are  again  attracted,  and  so  vibrate  to 
and  fro. 

By  another  arrangement  small  figures  or  dolls  cut  out 
of  pith  can  be  made  to  dance  up  and  down  between  a 
metal  plate  hung  horizontally  from  the  knob  of  the 
machine,  and  another  flat  plate  an  inch  or  two  lower  and 
communicating  with  "  earth." 

The  effect  of  points  in  discharging  electricity  from 
the  surface  of  a  conductor  may  be  readily  proved  by 
numerous  experiments.  If  the  machine  be  in  good 
working  order,  and  capable  of  giving,  say,  sparks  four 
inches  long  when  the  knuckle  is  presented  to  the  knob, 
it  will  be  found  that,  on  fastening  a  fine  pointed  needle 

*  Invented  in  1752  by  Franklin,  for  the  purpose  of  warning  him  of  the 
presence  of  atmospheric  electricity,  drawn  from  the  air  above  his  house  by  a 
pointed  iron  rod. 


CHAP.  I.]    ELECTRICITY  AND  MAGNETISM. 


47 


to  the  conductor,  it  discharges  the  electricity  so  effect- 
Dally  at  its   point  that  only  the  shortest  sparks  can  be 


Fig.  26. 

drawn  at  the  knob,  while  a  fine  jet  or  brush  of  pale 
blue  light  will  appear  at  the  point.  If  a  lighted  taper 
be  held  in  front  of  the  point, 
the  flame  will  be  visibly  blown 
aside  (Fig.  26)  by  the  streams 
of  electrified  air  repelled  from 
the  point.  These  air-currents 
can  be  felt  with  the  hand. 
They  are  due  to  a  mutual  re- 
pulsion between  the  electrified 
air-particles  near  the  point  and 
the  electricity  collected  on  the 
point  itself.  That  this  mutual 
reaction  exists  is  proved  by 
the  electric  fly  or  electric 
reaction -mill  of  Hamilton 
(Fig.  27),  which  consists  of 


Fig.  27. 


a  light  cross  of  brass  or  straw,  suspended  on  a  pivot, 


48  ELEMENTARY  LESSONS  ON        [CHAP.  I. 

and  having  the  pointed  ends  bent  round  at  right 
angles.  When  placed  on  the  prime  conductor  of  the 
machine,  or  joined  to  it  by  a  chain,  the  force  of 
repulsion  between  the  electricity  of  the  points  and  that 
on  the  air  immediately  in  front  of  them  drives  the 
mill  round  in  the  direction  opposite  to  that  in  which  the 
points  are  bent 

Another  favourite  way  of  exhibiting  electric  repulsion 
is  by  means  of  a  doll  with  long  hair  placed  on  the 
machine ;  the  individual  hairs  stand  on  end  when  the 
machine  is  worked,  being  repelled  from  the  head,  and  from 
one  another.  A  paper  tassel  will  behave  similarly  if 
hung  to  the  prime  conductor.  The  most  striking  way 
of  showing  this  phenomenon  is  to  place  a  person  upon 
a  glass -legged  stool,  making  him  touch  the  knob  of 
the  machine ;  when  the  machine  is  worked,  his  hair, 
if  dry,  will  stand  on  end.  Sparks  will  pass  freely 
between  a  person  thus  electrified  and  one  standing 
upon  the  ground. 

The  sparks  from  the  machine  may  be  made  to  kindle 
spirits  of  wine  or  ether,  placed  in  a  metallic  spoon, 
connected  by  a  wire,  with  the  nearest  metallic  conductor 
that  runs  into  the  ground.  A  gas  jet  may  be  lit  by 
passing  a  spark  to  the  burner  from  the  finger  of  the  per- 
son standing,  as  just  described,  upon  an  insulating  stool. 

44.  Armstrong's  Hydro-Electrical  Machine. — 
The  friction  of  a  jet  of  steam  issuing  from  a  boiler, 
through  a  wooden  nozzle,  generates  electricity.  In 
reality  it  is  the  particles  of  condensed  water  in  the  jet 
which  are  directly  concerned.  Sir  W.  Armstrong,  who 
investigated  this  source  of  electricity,  constructed  a 
powerful  apparatus,  known  as  the  hydro -electrical 
machine  (Fig.  28),  capable  of  producing  enormous 
quantities  of  electricity,  and  yielding  sparks  five  or  six 
feet  long.  The  collector  consisted  of  a  row  of  spikes, 
placed  in  the  path  of  the  steam  jets  issuing  from  the 
nozzles,  and  was  supported,  together  with  a  brass  ball 


CHAP,  i.]     ELECTRICITY  AND  MAGNETISM. 


which  served  as  prime-conductor,  upon  a  glass  pillar. 
The  nozzles  were  made  of  wood,  perforated  with  a 
crooked  passage  in  order  to  increase  the  friction  of 
the  jet  against  the  sides. 


Fig.  28. 

45.  Convection -Induction  Machines. — There  is  another 
class  of  electrical  machine,  differing  entirely  from  those  we  have 
been  describing,  and  depending  upon  the  employment  of  a  small 
initial  charge  which,  acting  inductively^  produces  other  charges, 
which  are  then  conveyed  by  the  moving  parts  of  the  machine  to 
some  other  point  where  they  can  increase  the  initial  charge,  or 
furnish  a  supply  of  electricity  to  a  suitable  collector.  Of  such 
instruments  the  oldest  is  the  Electrophorus  of  Volta,  explained 
fully  in  Lesson  III.  Bennet,  Nicholson,  Darwin,  and  others, 


So  ELEMENTARY  LESSONS  ON          [CHAP.  i. 

devised  pieces  of  apparatus  for  accomplishing  by  mechanism  that 
which  the  electrophorus  accomplishes  by  hand.  Nicholson's 
revolving  doubler  consists  of  a  revolving  apparatus,  in  which 
an  insulated  carrier  can  be  brought  into  the  presence  of  an 
electrified  body,  there  touched  far  an  instant  to  remove  its 
repelled  electricity,  then  carried  forward  with  its  acquired  charge 
towards  another  body,  to  which  it  imparts  its_charge,  and  which 
in  turn  acts  inductively  on  it,  giving  it  an  opposite  charge  which 
it  can  convey  to  the  first  body,  thus  increasing  its  initial  charge 
at  every  rotation.  Similar  instruments  have  been  contrived  by 
Varley,  Sir  W.  Thomson  (the  "  replenisher "),  Topler,  Carre, 
and  Holtz.  The  two  latter  are  perfectly  continuous  in  their 
action,  and  have  been  well  described  as.  continuous  elutrophori. 
The  machine  of  Holtz  has  come  into  such  general  use  as  to 
deserve  explanation. 

46.  flbltz's  Influence  Machine. — The  action  of  this  machine 
is  not  altogether  easy  to  grasp,  though  in  reality  simple  enough 
.when  carefully  explained.  The  machine  in  its  latest  form 
consists  (see  Fig.  29)  of  two  plates,  one,  A,  fixed  by  its  edges  , 
the  other,  B,  mounted  on  an  axis,  and  requiring  to  be  rotated 
at  a  high  speed  by  a  band  and  driving  pulley.  There  are  two 
holes  or  windows,  P  and  P ,  cut  at  opposite  points  of  the  fixed 
plate.  Two  pieces  varnished  paper, /and/',  are  fastened  to  the 
plate  above  the  window  on  the  left  and  below  the  one  on  the 
right.  These  pieces  of  paper  or  armatures  are  upon  the  side  of 
the  fixed  plate  away  from  the  movable  disc,  or,  as  we  may  say, 
upon  the  back  of  the  plate.  They  are  provided  with  narrow 
tongues  which  project  forward  through  the  windows  towards  the 
movable  disc,  which  they  nearly  touch  with  their  protruding 
points.  The  disc  must  rotate  in  the  opposite  direction  to  that 
in  which  these  tongues  point.  On  the  front  side  of  the  moving 
disc,  and  opposite  the  forward  edges  of  the  two  armatures, 
stands  an  oblique  metal  conductor,  D,  which  need  not  be 
insulated.  It  has  metal  combs  or. spikes  projecting  towards  the 
disc.  On  the  right  and  left,  supported  on  insulating  holders, 
are  two  horizontal  metal  combs,  joined  to  two  metal  rods 
terminated  with  brass  balls,  m,  «,  which  in  this  form  of  machine 
merely  constitute  a  discharging  apparatus  and  are  not  concerned 
in  the  action  of  the  machine.  In  some  forms  of  Holtz  machine 
there  is  no  diagonal  conductor  D ;  and  as  the  discharging 
apparatus  has  then  to  serve  both  functions,  the  balls  tnt  //,  must 
in  these  forms  of  machine  touch  one  another  before  the  machine 


CHAP,  i.]  ELECTRICITY  AND  MAGNETISM. 


will  charge  itself.  To  work  the  machine  a  small  initial  charge 
must  be  given  by  an  electrophorus,  or  by  a  rubbed  glass  rod,  to 
one  of  the  two  armatures.  The  disc  is  then  rapidly  rotated  ; 

and  it  is  found  that 
after  A  few  turns 
the  exertion  required 
to  keep  up  the  ro- 
tation increases- 
greatly :  at  the  same 
moment  pale  blue 
brushes  of  light  are 
seen  to  issue  fiom 
the  points,  and,  on 
separating  the  brass 
balls,  a  torrent  of 
brilliant  sparks  darts 
across  the  interven- 
ing space.  The 
action  of  the  m  achine 

Fig-  2?'  is  as  follows.     Sup- 

pose a  small  +  charge  to  be  imparted  at  the  outset  to  the  right 
armature  f  ;  this  charge  acts  inductively  across  the  intervening 
glass  and  air  upon  the  comb  at  the  lower  end  of  the  diagonal 
conductor  D,  repels  electricity  through  D,  leaving  the  lower 
points  negatively  electrified.  These  discharge  negatively, 
electrified  air  upon  the  front  surface  of  the  movable  disc,  while 
the  repelled  +  charge  passes  up  along  D,  and  is  discharged 
through  the  upper  comb  upon  the  front  face  of  the  movable 
disc.  Here  it  acts  inductively  upon  the  paper  armature  f, 
causing  that  part  which  is  opposite  the  comb  to  be  negatively 
charged,  and  repelling  a  +  charge  into  its  farthest  part,  viz.  into1 
the  tongue,  which  slowly  discharges  a  +  charge  upon  the  back- 
of  the  moving  disc.  If  now  the  disc  be  turned  round,  this  + 
charge  on  the  back  comes  over,  in  the  direction  indicated  by  the 
arrow,  from  the  left  to  the  right  side  ;  and,  when  it  gets  opposite 
':he  right  tongue,  is  discharged  into  the  armature/',  increasing 
its  charge,  and  thereby  helps  that  armature  to  act  still  more 
strongly  than  before.  Meantime  the  -  charge,  which  we  saw 
had  been  induced  in  the  left  armature  f,  has  in  turn  reacted  on 
the  upper  comb,  causing  it  to  emit  more  powerfully  than  before- 
a  +  charge  from  its  points,  and  drawing  electricity  through  the 
diagonal  rod.  The  combs  at  the  two  ends  of  this  rod  therefore 


52  ELEMENTARY  LESSONS  ON          [CHAP.  i. 


both  emit  electrified  streams  of  air,  the  upper  one  charging  the 
upper  portion  of  the  front  of  the  rotating  disc  positively,  the 
lower  one  charging  the  lower  portion  of  the  disc  negatively. 
The  back  of  the  rotating  disc  is  at  the  same  time  similarly 
charged ; .  and  the  charges  carried  round  on  the  back  surface 
serve  to  increase  the  charges  on  the  two  armatures.  Hence  a 
very  small  initial  charge  is  speedily  raised  to  a  maximum,  the 


Fig.  290, 

limit  being  reached  when  the  electrification  of  the  armatures  is 
so  great  that  the  leakage  of  electricity  at  their  surface  equals 
the  gain  by  induction  and  convection.  The  charges  let  off  by 
the  spikes  of  the  diagonal  conductor  upon  the  front  surface  of 
the,  moving  disc  are  carried  round  and  discharged  into  the  right 
and  left  conductors  of  the  discharging  apparatus,  by  means  of 
the  horizontal  combs  which  collect  the  charges  exactly  as  ex- 
plained on  p.  43.  Two  small  Leyden  jars  are  usually  added 
to  increase  the  density  of  the  sparks  that  pass  between  m  and  «. 


CHAP.  L]    ELECTRICITY  AND  MAGNETISM.  53 

In  some  recent  Holtz  machines,  a  number  of  rotating  discs 
fixed  upon  one  common  axis  are  employed,  and'  the  whole  is 
enclosed  in  a  glass  case  to  prevent  access  of  damp.  A  small 
disc  of  ebonite  is  now  usually  fixed  to  the  axis,  and  provided 
with  a  rubber  in  order  to  keep  up  the  initial  charge.  Iloltz  has 
lately  constructed  a  machine  with  thirty-two  plates. 

Mascart  has  shown  the  interesting  fact  that  the  Holtz  machine  is  reversiblt 
ia  its  action  ;  that  is  to  say,  that  if  a  continuous  supply  of  the  two  electricities 
(furnished  by  another  machine)  be  communicated  to  the  armatures,  the 
movable  plate  will  be  thereby  set  in  rotation,  and  will  turn  in  an  opposite 
sense. 

Riglii  has  shown  that  a  Holtz  machine  can  yield  a  continuous  current  like 
a  voltaic  battery,  the  strength  of  the  current  being  nearly  proportional  to 
the  velocity  of  rotation.  It  was  found  that  the  electromotive  force  of  a  machine 
was  equal  to  that  of  52,000  Daniell's  cells,  or  nearly  5^,000  volts,  at  all  speed:.. 
Tlie  resistance,  when  the  machine  made  120  revolutions  per  minute,  was 
2180  million  ohms  ;  but  only  646  million  ohms  when  making  450  revolutions 
per  minute. 

Voss  has  lately  constructed  a  simple  machine  very  like  Fig.  29,  but  on 
Topler's  plan,  having  small  metallic  buttons  affixed  to  the  front  of  the  rotating 
plate,  these  buttons  being  lightly  touched,  while  rotating,  by  small  metal 
brushes  fixed  upon  the  combs,  thus  providing  by  friction  a  minute  initial 
charge.  In  this  machine  there  are  no  windows,  but  small  metal  arms  attached 
to  the  paper  armatures  and  furnished  with  small  brushes  of  metal  foil  are 
brought  round  to  the  front  of  the  rotating  plate,  and  touch  the  buttons  as  they 
pass.  The  buttons  therefore  act  as  carriers  of  charges  that  are  induced  in 
them  by  their  being  touched  whilst  under  inductive  influence. 

46  (bts).  Wimshurst's  Influence  Machine.  —  Still  more 
recent  is  the  machine  of  Wimslmrst  (Fig.  29a)  in  v/hich  the 
two  plates  rotate  in  opposite  directions.  Each  plate  has  a 
series  of  small  slips  of  thin  metal  foil  upon  it,  which  serve  both 
as  carriers  and  as  armatures.  There  are  two  uninsulated 
diagonal  conductors  at  the  front  and  back  ;  and  two  insulated 
collecting  combs  at  the  right  and  left,  connected  with  a 
discharging  apparatus.  Each  little  carrier  is  touched  by  an 
uninsulated  brush  as  it  passes  opposite  the  charged  carrier  ol 
the  other  disc,  and  each  thereby  has  a  charge  induced  in  it 
.which  it  carries  over  to  the  collecting  comb  on  the  right  or  left. 

LESSON  VI. — The  Ley  den  Jar  and  other  condensers. 

47.  It  was  shown  in  previous  lessons  that  the  opposite 
charges  of  electricity  attract  one  another  ;  that  electricity 
cannot  flow  through  glass  ;  and  that  yet  electricity  can 
act  across  glass  by  induction.  Two  suspended  pith- 
balls,  one  electrified  positively  and  the  other  negatively, 
will  attract  one  another  across  the  intervening  air.  If 
a  plate  of  glass  be  put  between  them  they  will  still 


34  ELEMENTARY  LESSONS  ON         [CHAP,  i, 

attract  one  another,  though  neither  they  themselves  nor 
the  electric  charges  on  them  can  pass  through  the  glass. 
If  a  pith-ball  electrified  with  a  -  charge  be  hung  inside  a 
dry  glass  bottle,  and  a  rubbed  glass  rod  be  held  outside, 
the  pith-ball  will  rush  to  the  side  of  the  bottle  nearest  to 
the  glass  rod,  being  attracted  by  the  +  charge  thus 
brought  near  it.  If  a  pane  of  glass  be  taken,  and  a  piece 
of  tinfoil  be  stuck  upon  the  middle  of  each  face  of  the 
pane,  and  one  piece  of  tinfoil  be  charged  positively, 
and  the  other  negatively,  the  tv/o  charges  will  attract 
one  another  across  the  glass,  and  v/ill  no  longer  be  found 
to  be  free.  If  the  pane  is  set  up  on  edge,  so  that  neither 
piece  of  tinfoil  touches  the  table,  it  will  be  found  that 
hardly  any  electricity  can  be  got  by  merely  touching  either 
of  the  foils,  for  the  charges  are  "  bound,"  so  to  speak, 
by  each  other's  attractions  ;  each  charge  is  inducing  the 
other.  In  fact  it  will  be  found  that  these  two  pieces  of 
tinfoil  may  be,  in  this  manner,  charged  a  gieat  deal 
more  strongly  than  either  of  them  could  possibly  be 
if  it  were  stuck  to  a  piece  of  glass  alone,  and  then  elec- 
trified. In  other  words,  the  capacity  of  a  conductor  is 
greatly  increased  when  it  is  placed  near  to  a  conduct ot 
electrified  with  the  opposite  kind  of  charge*  If  its 
capacity  is  increased,  a  greater  quantity  of  electricity 
may  be  put  into  it  before  it  is  chnrged  to  a  high  degiee 
of  potential.  Hence,  such  an  arrangement  for  holding 
a  large  quantity  of  electricity  may  be  called  a  con- 
denser or  accumulator  of  electricity. 

48.  Condensers. — Next,  suppose  that  we  have  two 
brass  discs,  A  and  B  (Fig.  30),  set  upon  insulating 
steins,  and  that  a  glass  plate  is  placed  between  them. 
Let  B  be  connected  by  a  wire  to  the  knob  of  an  electrical 
machine,  and  let  A  be  joined  by  a  wire  to  "  earth."  The 
+  charge  upon  B  will  act  inductively  across  the  glass 
plate  on  A,  and  will  repel  electricity  into  the  eaith, 
leaving  the  nearest  face  of  A  negatively  electrified. 
This  -  charge  on  A  will  attract  the  +  chaige  oi 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM. 


55 


B  to  the  side  nearest  the  glass,  and  a  fresh  supply  of 
electricity  will  come  from  the  machine.  Thus  this  ar- 
rangement will  become  an  accumulator  or  condenser. 
If  the  two  brass  discs  are  pushed  up  close  to  the  glass 
plate  there  will  be  a  still  stronger  attraction  between  the 
+  and  —  charges,  because  they  are  now  nearer  one 
another,  and  the  inductive  action  will  be  greater ;  hence 
a  still  larger  quantity  can  be  accumulated  in  the  plates. 
We  see  then  that  the  capacity  of  an  accumulator  is 
increased  by  bringing  the  plates  near  together.  If 
now,  while  the  discs  are  strongly  charged,  the  wires 
are  removed  and  the  discs  are  drawn  backwards 
from  one  another,  the  two  charges  will  not  hold 
one  another  bound  so  strongly,  and  there  will  be  more 
free  electrification 
than  before  over 
their  surfaces.  This 
would  be  rendered 
evident  to  the  ex- 
perimenter by  the 
little  pith-ball  elec- 
troscopes fixed  to 
them  (see  the  Fig.), 
which  would  fly  out  F;gt  „ 

as  the  brass  discs 

were  moved  apart.  We  have  put  no  further  charge  on 
the  disc  B,and  yet,  from  the  indications  of  the  electroscope, 
we  should  conclude  that  by  moving  it  away  from  disc  A 
it  has  become  electrified  to  a  higher  degree.  The  fact  is, 
that  while  the  conductor  B  was  near  the  -  charge  of  A 
the  capacity  of  B  was  greatly  increased,  but  on  moving 
it  away  from  A  its  capacity  has  diminished,  and  hence 
the  same  quantity  of  electricity  now  electrifies  it  to  a 
Ivgher  degree  than  before.  The  presence,  therefore,  of 
an  earth -connected  plate  near  an  insulated  conductor 
increases  its  capacity,  and  permits  it  to  accumulate  a 
greater  charge  by  attracting  and  condensing  the  elec- 


56  ELEMENTARY  LESSONS  ON         [CHAP.  f. 

tricity  upon  the  face  nearest  the  earth-plate,  the  surface- 
density  on  this  face  being  therefore  very  great.  Such 
an  arrangement  is  sometimes  called  a  condenser,  some- 
times an  accumulator.  We  shall  call  such  an  arrange- 
ment a  condenser  when  the  object  of  the  earth-connected 
plate  is  to  increase  the  surface-density  of  the  charge 
upon  one  face  of  the  insulated  conductor.  The  term 
accumulator  is  now  more  often  applied  to  batteries  for 
storing  the  energy  of  electric  currents  (Art.  415). 

The  stratum  of  air  between  the  two  discs  will  suffice 
to  insulate  the  two  charges  one  from  the  other.  The 
brass  discs  thus  separated  by  a  stratum  of  air  constitute 
an  air-condenser.  Such  condensers  were  first  devised 
by  Wilke  and  Aepinus. 

49.  Dielectrics. — In  these  experiments  the  sheet  of 
glass  or  layer  of  air  plays  an  important  part  by  permitting 
the  inductive  electric  influences  to  act  across  or  through 
them.  On  account  of  this  property  these  substances 
were  termed  by  Faraday  dielectrics.  All  dielectrics 
are  insulators,  but  equally  good  insulators  are  not  neces- 
sarily equally  good  dielectrics.  Air  and  glass  are  far  better 
insulators  than  ebonite  or  paraffin  in  the  sense  of  being 
much  worse  conductors.  But  induction  takes  place  better 
across  a  slab  of  glass  than  across  a  slab  of  ebonite  or 
paraffin  of  equal  thickness,  and  better  still  across  these 
than  across  a  layer  of  air.  In  other  words,  glass  is  a 
better  dielectric  than  ebonite,  or  paraffin,  or  air. 
Those  substances  which  are  good  dielectrics  are  said  to 
possess  a  high  inductive  capacity. 

6.O.  Capacity  of  a  Condenser.  —  It  appears, 
therefore,  that  the  capacity  of  a  condenser  will  depend 
upon — 

(1)  The  size  and  form  of  the  metal  plates  or  coatings. 

(2)  Thethinness  of  the  stratum  of  dielectric  between 

them  ;  and 

(3)  The  inductive  capacity  of  the  dielectric. 

61.  The  Lieyden  Jar. — The  Leyden  Jar,  called  after 


CHAP,  i.]     ELECTRICITY  AND  MAGNETISM. 


57 


the  city  where  it  was  invented,  is  a  convenient  form  of 

condenser.      It  usually  consists  (Fig.  31)  of  a  glass  jar 

coated  up  to  a  certain  height  on  the  inside  and  owtside 

with    tinfoil.       A   brass  knob 

fixed  on  the  end   of  a    stout 

brass  wire   passes   downward 

through   a  lid  or  top   of  dry 

well -varnished      wood,     and 

communicates  by  a  loose  bit 

of  brass  chain  with  the  inner 

coating    of  foil.      To    charge 

the  jar    the  knob   is  held  to 

the    prime    conductor   of   an 

electrical  machine,  the  outer 

coating  being   either  held  in 


Fig.  31 


the  hand  or  connected  to  "  earth ''  by  a  wire  or  chain. 
When  a  +  charge  of  electricity  is  imparted  thus  to  the 
inner  coating,  it  acts  inductively  on  the  outer  coating, 
attracting  a  -  charge  into  the  face  of  the  outer  coating 
nearest  the  glass,  and  repelling  a  +  charge  to  the  outside 
of  the  outer  coating,  and  I  hence  through  the  hand  or  wire 
to  earth.  After  a  few  moments  the 
jar  will  have  acquired  its  full  charge, 
the  outer  coating  being  -  and  the 
inner  +.  If  the  jar  is  of  good  glass, 
and  dry,  and  free  from  dust,  it  will 
retain  its  charge  for  many  hours  or 
days.  But  if  a  path  be  provided  by 
which  the  two  mutually  attracting 
electricities  can  flow  to  one  another, 
they  will  do  so,  and  the  jar  will  be 
instantaneously  discharged.  If  the 
outer  coating  be  grasped  with  one 
Fif  3*V.  hand,  and  the  knuckle  of  the  other 
hand  be  presented  to  the  knob  of  the  jar,  a  bright 
s?ark  will  pass  between  the  knob  and  the  knuckle 
With  a  sharp  report,  and  at  the  same  moment  a  convulsive 


58  ELEMENTARY  LESSONS  ON         [CHAP,  t. 

"  shock  "  will  be  communicated  to  the  muscles  of  the 
wrists,  elbows,  and  shoulders.  A  safer  means  of  dis- 
charging the  jar  is  afforded  by  the  discharging-  tonga 
or  discharger  (Fig.  32),  which  consists  of  a  jointed 
brass  rod  provided  with  brass  knobs  and  a  glass  handle. 
One  knob  is  laid  against  the  outer  coating,  the  other  is 
then  brought  near  the  knob  of  the  jar,  and  a  bright 
snapping  spark  leaping  from  knob  to  knob  announces 
that  the  two  accumulated  charges  have  flowed  together, 
completing  the  discharge. 

52.  Discovery   of  the   Ley  den   Jar. — The   dis- 
covery of  the   Leyden   jar  arose   from  the  attempt  of 
Musschenbroek  and   his   pupil   Cuneus1   to    collect  the 
supposed   electric   "  fluid "   in   a   hottle   half  filled  with 
water,  which  was  held  in  the  hand  and  was  provided 
with  a  nail  to  lead  the  "  fluid  "  down  through  the  cork 
to   the   water   from    the   electric    machine..     Here   the 
water  served  as  an  inner  coating  and  the  hand  as  an 
outer  coating  to  the  jar.     Cuneus  on  touching  the  nail 
received    a   shock.     This  accidental  discovery  created 
the  greatest  excitement  in  Europe  and  America. 

53.  Residual    Charges.  —  If    a    Leyden    jar    be 
charged  and  discharged  and  then  left  for  a  little  time  to 
itself,  it  will  be  found  on  again  discharging  that  a  small 
second   spark  can   be   obtained.     There  is   in   fact  a 
residual  charge  which  seems  to  have  soaked  into  the 
glass  or  been  absorbed      The  return  ot   the  residual 
charge  is  hastened  by  tapping  the  jar.     The  amount  of 
the  residual  charge  varies  with  the  time  that  the  jar  has 
been  left  charged  ;  it  also  depends  on  the  kind  of  the  glass 
of  which  the  jar  is  made.     There  is  no  residual  charge 
discoverable  in  an  air-condenser  after  it  has  once  been 
discharged. 

54.  Batteries  of  Leyden  Jars. — A  large  Leyden 
jar  will  give  a  more  powerful  shock  than  a  small  one, 

1  The  honour  of  the  invention  of  the  jar  is  also  claimed  for  Kleist, 
Bishop  of  Poinerania- 


CHAP,!.]      ELECTRICITY  AND  MAGNETISM. 


59 


for  a  larger  charge  can  be  put  into  it :  its  capacity  is 
greater.  A  Leyden  jar  made  of  /////;  glaus  has  a 
greater  capacity  as  an  accumulator  than  a  thick  one  of 
the  same  size ;  but  if  it  is  too  thin  it  will  be  destroyed 
when  powerfully  charged  by  a  spark  actually  piercing 
the^glass.  "  Toughened "  glass  is  less  easily  pierced 
than  ordinary  glass,  and  hence  Leyden  jars  made 


Fig.  33. 

of  it  may  be  made  thinner,  and  so  will  hold  a  greater 
charge. 

If,  however,  it  is  desired  to  accumulate  a  very  great 
charge  of  electricity,  a  number  of  jars  must  be  em- 
ployed, all  their  inner  coatings  being  connected  together, 
and  all  their  outer  coatings  being  united.  This  arrange- 
ment is  called  a  Battery  of  Leyden  jars,  or  Leyden 


ELEMENTARY  LESSONS  ON         [CHAP.  I. 


battery,  Fig.  33.  As  it  has  a  large  capacity  it  will 
require  a  large  quantity  of  electricity  to  charge  it  fully. 
When  charged  it  produces  very  powerful  effects.;  its 
spark  will  pierce  glass  readily,  and  every  care  must  be 
taken  to  avoid  a  shock  from  it  passing  through  the 
person,  as  it  might  be  fatal.  The  "  Universal  Dis- 
charger "  as  employed  with  the  Leyden  battery  is  shown 
in  the  figure. 

55.  Seat  of  the  charge.  —  Benjamin  Franklin 
discovered  that  the  charges  of  the 
Leyden  jar  really  resided  on  the 
surface  of  the  glass,  no.t  on  the 
metallic  coatings.  This  he  proved 
by  means  of  a  jar  whose  coatings 
could  be  removed,  Fig.  34.  The 
jar  was  charged  and  placed  upon 
an  insulating  stand.  The  inner 
coating  was  then  lifted  out,  and  the 
glass  jar  was  then  taken  out  of  the 
outer  coating.  Neither  coating 
was  found  to  be  electrified  to  any 
extent,'  but  on  again  putting  the  jar 
together  it  was  found  to  be  highly 
charge.d.  The  charges  had  all  the 
time  remained  upon  the  inner  and 
outer  surfaces  of  the  glass  dielectric. 
56.  Dielectric  Strain. — Fara- 
I  day  proved  that  the  medium  across 
which  induction  takes  place  really 
plays*  an  important  part  in  the 
phenomena.  It  is'  now  known 
dieletrics  across  which  inductive  actions  are  at 
thereby  strained.1  Inasmuch  as  a  good 
a  good  dielectric,  it  is  clear  that  it  is  not 


that  all 
work    are 
vacuum  is 


1  In  the  exact  sciences  a  slraiu  means  an  alteration  of  form  or  volume 
due  to  the  application  of  a  stress.  A  stress  is  the  force,  pressure,  or  other 
agency  which  produces  a  strain. 


CHAP.  T.I      ELECTRICITY  AND- MAGNETISM.  6l 

necessarily  the  material  particles  of  the  dielectric  sub- 
stance that  are  thus  affected  ;  hence  it  is  believed  that 
electrical  phenomena  are  due  to  stresses  and  strains  in 
the  so-called  "aether,"  the  thin  medium  pervading  all 
matter  and  all  space,  whose  highly  elastic  constitution 
enables  it  to  convey  to  us  the  vibrations  of  light  though 
it  is  millions  of  times  less  dense  than  the  air.     As  the 
particles  of  bodies  are  intimately  surrounded  by";ether," 
the  strains  of  the  "  aether "  are   also   communicated  to 
the  particles   of  bodies,  and   they  too  suffer  a  strain. 
The  glass  between   the   two   coatings   of  tinfoil   in  the 
Leyden  jar  is  actually  strained  or  squeezed  between  the 
attracting   charges  of  electricity.      When   an   insulated 
charged  ball  is  hung  up  in  a' room  an  equal  amount  of 
the  opposite  kind  of  electricity  is  attracted  to  the  inside 
of  the  walls,  and  the  air  between  the  ball  and  the  walls 
is  strained  (electrically)  like  the  glass  of  the  Leyden 
jar.      If  a  Leyden  jar  is  made  of  thin  glass  it  may  give 
way  under  the  stress  ;   and  when  a  Leyden  jar  is  dis- 
charged the  layer  of  air  between  the  knob  of  the  jar  and 
the  knob  of  the  discharging  tongs   is   more  and  more 
strained  as  they  are  approached  towards  one  another, 
till  at  last  .the  stress  becomes  too  great,  and  the  layer  of 
air  gives  way,  and  is  "  perforated "  by  the  spark  that 
discharges  itself  across.      The  existence  of  such  stresses 
enables  us  to  understand  the  residual  charge  of  Leyden 
jars  in  which  the  glass  does  not  recover  itself  all  at  once, 
by  reason  of  its  viscosity,  from  the  strain  to  which  it 
has   been   subjected.      This    hypothesis,   that    electric 
force  acts  across  space  in  consequence  of  the 
transmission    of   stresses    and    strains    in    the 
medium  with  which  space  is  filled,  is  now  entirely 
superseding  the  old  theory  of  action-at-a-distance,  which 
was  logically  unthinkable,  and  which,  moreover,  failed  to 
account  for  the  facts  of  observation. 


62  ELEMENTARY  LESSONS  ON         [CHAP.  i. 


LESSON  VII. — Other  Sources  of  Electricity. 

57.  It    was    remarked    at    the    close    of    Lesson    I. 
(p.  10),  that  friction  was  by  no  means  the  only  source 
of  electricity.     Some  of  the  other  sources  will  now  be 
named. 

58.  Percussion. — A    violent    blow    struck    by    one 
substance    upon    another    produces    opposite    electrical 
states   on  the  two  surfaces.      It   is  possible   indeed  to 
draw  up  a  list   resembling  that   of  Art.   5,  in   such   an 
order -that  each  substance  will  take  a  +  charge,  on  being 
struck  with  one  lower  on  the  list.      Erman,  who  drew  up 
such  a  list  for  a  number  of  metals,  remarked  that  the 
order  was  the  same  as  that  of  the  thermo-electric  series 
given  in  Article  381. 

59.  Vibration. — Volpicelli    showed   that   vibrations 
set  up  within   a  rod  of  metal  coated  with   sulphur  or 
other    insulating   substance,    produced    a    separation   of 
electricities  at  the  surface  separating  the  metal  from  the 
non-conductor. 

60.  Disruption  and  Cleavage. — If  a  card  be  torn 
asunder  in  the  dark,  sparks  are  seen,  and  the  separated 
portions,  when  tested  with  an  electroscope,  will  be  found 
to  be  electrical.     The  linen  faced  with  paper  used  in 
making   strong   envelopes   and   for  paper   collars,  shows 
this  very  well.      Lumps  of  sugar,  crunched  in  the  dark 
between  the  teeth,  exhibit   pale  flashes  of  light.     The 
sudden  cleavage  of  a  sheet  of  mica  also  produces  sparks, 
and  both  lamina?  are  found  to  be  electrified. 

61.  Crystallisation    and    Solidification. —  Many 
substances,  after  passing  from  the  liquid  to  the  solid  state, 
exhibit  electrical  conditions.      Sulphur  fused  in  a  glass 
dish  and   allowed  to  cool  is  violently  electrified,  as  may 
be  seen  by  lifting  out  the  crystalline  mass  with  a  glass  rod. 
Chocolate  also  becomes  electrical  during   solidification. 
When  arsenic  acid  crystallise;*  out  from  its   solution  in 


CHAP,  i,J       ELECTRICITY  AND  MAGNETISM.  63 

hydrochloric  acid,  the  formation  of  each  crystal  is  accom- 
panied by  a  flash  of  light,  doubtless  due  to  an  electrical 
discharge*  A  curious  case  occurs  when  the  sulphate  of 
copper  and  potassium  is  fused  in  a  crucible.  It  solidi- 
fies without  becoming  electrical,  but  on  cooling  a  little 
further  the  crystalline  mass  begins  to  fly  to  powder  with 
an  instant  evolution  of  electricity, 

62.  Combustion. —  Volta  showed  that  combustion 
generated  electricity.     A  piece  of  burning  charcoal,  or  a 
burning  pastille,  such  as  is  used  for  fumigation,  placed  in 
connection  with  the  knob  of  a  gold-leaf  electroscope,  will 
cause  the  leaves  to  diverge.. 

63.  Evaporation.  —  The    evaporation     of    liquids 
is  often  accompanied  by  electrification,  the  liquid  and 
the  vapour  assuming  opposite  states.     A  few  drops  of  a 
solution  of  sulphate  of  copper  thrown  into  a  hot  plati- 
num   crucible   produce    violent    electrification    as   they 
evaporate, 

64.  Atmospheric  Electricity, — Closely  connected 
with  the  electricity  of  evaporation  is  the  atmospheric 
electricity  always  present  in  the  air,  and  due,  in  part 
at  least,  to  evaporation  going  on  over  the  oceans.     The 
subject   of   atmospheric   electricity  is  treated  of  sepa- 
rately in  Lesson  XXIV, 

65.  Pressure. — A  large  number  of  substances  when 
compressed  exhibit  electrification  on  their  surface.     Thus 
cork  becomes   +  when   pressed  against   amber,  gutta- 
percha,  and  metals ;    while  it  takes  a        charge  when 
pressed  against  spars  and  animal   substances,      Abbe 
Haiiy  found  that  a  crystal  of  calcspar  pressed  between 
the  dry  fingers,  so  as  to  compress  it  along  the  blunt 
edges  of  the  crystal,  became  electrical,  and  that  it  re- 
tained  its  electricity  for  some  days.     He  even  proposed 
to  employ  a  squeezed  suspended  crystal  as  an  electro- 
scope.    A  similar   property  is  alleged   of  mica,  topaz, 
and  fluorspar.     Pressure  also  produces  opposite  kinds  oi 
electrification  at  opposite  ends  of  a  crystal  of  tourmaline 


64  ELEMENTARY  LESSONS  ON         [CHAP.  i. 

and    of    other*  crystals    mentioned   in   the   next   para, 
graph. 

66.  Pyro-electricity. — There  are  certain  crystals 
which,  while  being  heated  or  cooled,  exhibit  electrical 
charges  at  certain  regions  or  poles.  Crystals  thus 
electrified  by  heating  or  cooling  are  said  to  be  pyro- 
electric.  Chief  of  these  is  the  Tourmaline,  whose 
power  of  attracting  light  bodies  to  its  ends  after  being 
heated  has  been  known  for  some  centuries.  It  is  alluded 
to  by  Theophrastus  and  Pliny  under  the  name  of  Lapis 
Lyncuritts.  The  tourmaline  is  a  hard  mineral,  semi- 
transparent  when  cut  into  thin  slices,  and  of  a  dark 
green  or  brown  colour,  but  looking  perfectly  black  and 
opaque  in  its  natural  condition,  and  possessing  the  power 
of  polarising  light.  It  is  usually  found  in  slightly  irregu- 
lar three-sided  prisms  which,  when  perfect,  are  pointed 
at  both  ends.  It  belongs  to  the  "  hexagonal "  system 
of  crystals,  but  is  only  hemihedral,  that  is  to  say,  has 
the  alternate  faces  only  developed.  Its  form  is  given 
in- Fig.  3'5,  where  a  general  view  is  first  shown,  the  two 
ends  A  and  B  being  depicted  in  separate  plans.  It  will 
be  noticed  that  these  two  ends  are  slightly  different 
from  each  other.  Each  is  made  up  of  three  sloping 
faces  terminating  in  a  point.  But  at  A  the  edges 
between  these  faces  run  down  to  the  corners  of  the 
prism,,  while  in  B  the  edges  between  the  terminal  faces 
run  down  to  the  middle  points  of  the  long  faces  of  the 
prism.  The  end  A  is  known  as  the  analogous  pole, 
and  B  as  the  antilogous  pole.  While  the  crystal  is 
rising  in  temperature  A  exhibits  +  electrification,  B  — ; 
but  if,  after  having  .been  heated,  it  is  allowed  to  cool, 
the  polarity  is  reversed ;  for  during  the  time  that  the 
temperature  is  railing  B  is  +  and  A  is  -.  If  the 
temperature  is  steady  .no  such  electrical  effects  are 
observed  either  at  high  or  lew  temperatures ;  and  the 
phenomena  cease  if  the  crystal  be  warmed  above  150° 
C.  This  is- not.  hcv/ever,  due,  as  Gaugain  declared,  to 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM. 


the  crystal  becoming  a  conductor  at  that  temperature ; 
for  its  resistance  at  even  higher  temperatures  is  still  so 
great  as  to  make  it  practically  a  non-conductor.  A 
heated  crystal  of  tourmaline  suspended  by  a  silk  fibre 
may  be  attracted  and  repelled  by  electrified  bodies,  or 
by  a  second  heated  tourmaline  ;  the  two  similar  poles 
repelling  one  another,  while  the  two  poles  of  opposite 
form  attract  one  another.  If  a  crystal  be  broken  up," 
each  fragment  is  found  to  uossess  also  an  analogous  and 
an  antilogous  pole. 

67.    Many  other   crystals   beside  the  tourmaline   are 
more  or  less  pyro-electric.     Amongst  these  are  silicate  of 


\\z 


r>g-  35- 

zinc  ("  electric  calamine  "),  boracite,  cane-su»ar,  quartz, 
tartrate  of  potash,  sulphate  of  quinine,  and  several  others. 
Boracite  crystallises  in  the  form  shown  in  Fig.  36,  which 
represents  a  cube  having  four  alternate  corners  trun- 
cated. The  corners  not  truncated  behave  as  analogous 
poles,  the  truncated  ones  as  antilogous.  This  peculiar 
skew- symmetry  or  hemihedry  is  exhibited  by  all  the 
crystals  enumerated  above,  and  is  doubtless  due  to  the 
same  molecular  peculiarity  which  determines  their  sin- 
gular electric  property,  and  which  also,  in  many  cases, 
determines  the  optical  behaviour  of  the  crystal  in 
polarised  light. 


66  ELEMENTARY  LESSONS  ON         [CHAP,  l 

68.  Animal  Electricity. — Several  species  of  crea- 
tures inhabiting  the  water  have  the  power  of  producing 
electric  discharges  by  certain  portions  of  their  organism. 
The  best  known  of  these  are  the  Torpedo,  the  Gym- 
notuS)  and  the  Silurus^  found  in  the  Nile  and  the 
Niger.  The  Raia  Torpedo,1  or  electric  ray,  of  which 

there  are  three  species  in- 
habiting the  Mediterranean 
and  Atlantic,  is  provided  with 
an  electric  organ  on  the  back 
of  its  head,  as  shown  in  Fig. 
37.  This  organ  consists  of 
laminae  composed  of  polygonal 
cells  to  the  number  of  800  or 
loop,  or  more,  supplied  with 
four  large  bundles  of  nerve 
fibres ;  the  under  surface  of 
the  fish  is  — ,  the  upper  + . 
In  the  G-ymnotus  electricus, 
or  Surinam  eel  (Fig.  38),  the 
electric  organ  goes  the  whole 
length  of  the  body  along  both 
sides.  It  is  able  to  give  a 
most  terrible  shock,  and  is  a 
formidable  antagonist  when  it 
has  attained  its  full  length  of 
5  or  6  feet.  Humboldt  gives 
a  lively  account  of  the  combats 
between  the  electric  eels  and 
the  wild  horses,  driven  by  the 
F;  natives  into  the  swamps  in- 

habited by  the  Gymnotus. 
Nobili,  Matteucci,  and  others,  have  shown  that  nerve- 

1  It  is  a  curious  point  that  the  Arabian  name  for  the  torpedo,  ra-ad, 
signifies  lightning.  This  is  perhaps  not  so  curious  as  that  the  Electro,  of 
the  Homeric  legends  should  possess  certain  qualities  that  would  tend  to 
suggest  that  she  is  a  personification  of  the  lightning.  The  resemblance 
between  the  names  electra  and  electron  (amber)  cancot  be  accidental. 


CHAP.  i.J     ELECTRICITY  AND  MAGNETISM.  67 

excitations  and  muscular  contractions  of  human  beings 
also  give  rise  to  feeble  discharges  of -electricity. 


Fig.  38. 

69.  Electricity  of  Vegetables. — Buf£  thought  he 
detected  electrification  produced  by  plant  life ;  the  roots 
and  juicy  parts  being  negatively,  and  the  leaves  posi- 
tively, electrified.     The  subject  has,  however,  been  little 
investigated. 

70.  Thermo-electricity.  —  Heat    applied    at    the 
junction   of  two   dissimilar   metals  produces   a  flow  of 
electricity  across  the  junction.     This  subject  is  discussed 
in  Lesson  XXXIV.  on  Thermo-electric  Currents. 

7L  Contact  of  dissimilar  Metala — Volta  showed 
that  the  contact  of  two  dissimilar  metals  produced 
opposite  kinds  of  electricity  on  the  two  surfaces,  one 
becoming  positively,  and  the -other  negatively,  electrified. 
This  he  proved  in  several  ways,  one  of  the  most  con- 
clusive proofs  being  that  afforded  by  his  condensing 
electroscope.  This  consisted  of  a  gold-leaf  elec- 
troscope combined  with  a  small  condenser.  A  metallic 
plate  formed  the  top  of  the  electroscope,  and  on  this 
was  placed  a  second  metallic  plate  furnished  with  a 
handle,  and  insulated  from  the  lower  one  by  being  well 
varnished  at  the  surface  (Fig.  68).  As  the  capacity  of 
such  a  condenser  is  considerable,  a  very  feeble  source 
may  supply  a  quantity  of  electricity  to  the  condenser  with- 
out materially  raising  its  potential,  or  causing  the  gold 
leaves  to  diverge.  But  if  the  upper  plate  be  lifted,  the 
capacity  of  the  lower  plate  diminishes  enormously,  and 


68  ELEMENTARY  LESSONS  ON        [CHAP,  t 

the  potential  of  its  charge  rises  as  shown  by  the  diverg- 
ence of  the  gold  leaves.  To  prove  by  the  condensing 
electroscope  that  contact  of  dissimilar  metals  does 
produce  electrification,  a  small  compound  bar  made  of 
two  dissimilar  metals — '  say  zinc  and  copper — soldered 
together,  is  held  in  the  hand,  and  one  end  of  it  is  touched 
against  the  lower  plate,  the  upper  plate  being  placed  in 
contact  with  the  ground  or  touched  with  the  finger. 
When  the  two  opposing  charges  have  thus  collected  in 
the  condenser  the  upper  plate  is  removed,  and  the 
diverging  of  the  gold  leaves  shows  the  presence  of  a 
free  charge,  which  can  afterwards  be  examined  to  see 
whether  it  be  +  or  -  .  For  a  long  time  the  existence 
of  this  electricity  of  contact  was  denied,  or  rather  it  was 
declared  to  be  due  (when  occurring  in  voltaic  combina- 
tions such  as  are  described  in  Lesson  XI J I.)  to  chemical 
actions  going  on  ;  whereas  the  real  truth  is  that  the 
electricity  of  contact  and  the  chemical  action  are  both 
due  to  molecular  conditions  of  the  substances  which 
come  into  contact  with  one  another,  though  we  do  not 
yet  know  the  precise  nature  of  the  molecular  conditions 
which  give  rise  to  these  two  effects.  Later  experiments, 
especially  those  made  with  the  delicate  electrometers  of 
Sir  W.  Thomson  (Fig.  101),  put  beyond  doubt  the  reality 
of  Volta's  discovery.  One  simple  experiment  explains  the 
method  adopted.  A  thin  strip  or 
needle  of  metal  is  suspended  so  as 
to  turn  about  a  point  C.  It  is  elec- 
trified  from  a  known  source.  Under 
it  are  placed  (Fig.  39)  two  semicii- 
cular  discs,  or  half-rings  of  dissimilar 
metals.  Neither  attracts  or  repels 
the  electrified  needle  until  the  two  are 
brought  into  contact,  or  connected  by 
a  third  piece  of  metal,  when  the  needle  immediately  turns, 
being  attracted  by  the  one  that  is  oppositely  electrified,and 
lepeiied  by  the  one  that  is  similarly  electrified  with  itself. 


CHAP,  i.]    ELECTRICITY  AND  MAGNETISM.  69 

72.  Volta  found,  moreover,  that  the  differences  of 
electric  potential  between  the  different  pairs  of  metals 
were  not  all  equal.  Thus,  while  zinc  and  lead  were 
respectively  +  and  -  to  a  slight  degree,  he  found  zinc 
and  silver  to  be  respectively  +  and  —  to  a  much  greater 
degree.  He  was  able  to  arrange  the  metals  in  a  series 
such  that  each  one  enumerated  became  positively  elec- 
trified when  placed  in  contact  with  one'  below  it  in  the 
series.  Those  in  italics  are  added  from  observations 
made  since  Volta's  time — 

CONTACT- SERIES  OF  METALS  (IN  AIR). 

+  So  Jin  n  i. 

Magnesium. 

Zinc. 

Lead. 

Tin. 

Iron. 

Copper. 

Silver. 

Gold. 

J'lalimnn. 

-  Graphite  (Carbon). 

Though  Volta  gave  rough  approximations,  the  actual 
numerical  values  of  the  differences  of  potential  for 
different  pairs  of  metals  have  only  lately  been  measured 
by  Ayrton  and  Perry,  a  few  of  whose  results  are  tabu- 
lated here — 

DifTci  ence  of  Potential 
(in  voll<=)t 

Zinc          1  -210 


Lead 
Tin 

Iron 

I       •»         •          •          '1^6 
Copper     J 

Platinum  j 
Carbon 


70  ELEMENTARY  LESSONS  ON         [CHAP.  I. 

The  difference  of  potential  between  zinc  and  carbon  is 
the  same  as  that  obtained  by  adding  the  successive 
differences,  or  1:09  volts.1  Volta's  observations  may 
therefore  be  stated  in  the  following  generalised  form, 
known  as  Volta's  Law.  The  difference  of  potential 
between  any  two  metals  is  equal  to  the  SUMI  of  the  differ- 
ences of  potentials  between  the  intervening  metals  in  the 
contact-series. 

It  is  most  important  to  notice  that  the  order  of  the 
metals  in  the  contact -series  in  air  is  almost  identical 
with  that  of  the  metals  arranged  according  to  their 
electro-chemical  power,  as  calculated  from  their  chemical 
equivalents  "and  their  heat  .of  combination  with  oxygen 
(see  Table,  Art.  422  (bis).  From  this  it  would  appear 
that  the  difference  of  potentials  between  a  metal  and  the 
air  that  surrounds  it  measures  the  tendency  of  that 
metal  to  become  oxidised  by  the  air.  If  this  is  so,  and 
if  (as  is  the  case)  the  air  is  a  bad  conductor  while  the 
metals  are  good  conductors,  it  ought  to  follow  that  when 
two  different  metals  touch  the)'  equalise  their  own 
potentials  by  conduction  but  leave  the  films  of  air  that 
surround  them  at  different  potentials.  All  the  exact 
experiments  yet  made  have  measured  the  difference  of 
potentials  not  between  the  metals  themselves,  but 
between  the  air  near  one  metal  and  that  near  another 
metal.  All  this  is  most  important  in  the  theory  of  the 
voltaic  cells.  Mr.  James  Brown  has  lately  demonstra  ed 
the  existence  on -freshly-cleaned  metal  surfaces  of  films 
of  liquid  or  condensed  gases,  and  has  shown  that 
polished  zinc  and  copper  when  brought  so  near  that 
their  films  touch  will  act  as  a  battery. 

73.  A  difference  of  potential  is  also  produced  by  the 
contact  of  two  dissimilar  liquids  with  one  another. 

A  liquid  and  a  metal  in  contact  with  one  another 
also  exhibit  a  difference  of  potential. 

\  For  the  definition  of  the  volt,  or  unit  of  difference  of  potential,  see  Art 
«• 


CHAP.  i.J    ELECTRICITY  AND  MAGNETISM.  71 

A  hot  metal  placed  in  contact  with  a  cold  piece  of 
the  same  metal  also  produces  a  difference  of  potential, 
electrical  separation  taking  place  across  the  surface  of 
contact. 

Lastly,  it  has  been  shown  Ity  Prof.  J.  J.  Thomson  that 
the  surface  of  contact  between-  two  non-conducting  sub- 
stances, such  as  sealing-wax  and  glass,  is  the  seat  of  a 
permanent  difference  of  potentials. 

74.  Magneto-electricity. — Electricity,  in  the  form 
of  currents  flowing  along  in  wires,  can  be  obtained  from 
magnets  by  moving  closed  conducting  circuits  in  their 
neighbourhood.      As-  this    source    of  electricity    yields 
currents  rather  than   statical,  charges  of  electricity,  the 
account  of  it  is-  deferred  to  Lesson  XXXVI. 

75.  Summary. — We   have   seen   in  the   preceding 
paragraphs  how    almost   all    conceivable  agencies  may 
produce  electrification  in  bodies.     The  most  important 
of  these -are  friction,  heat,  chemical  action,  magnetism, 
and  the  contact  of  dissimilar   substances.      We   noted 
that  the  production  of  electricity  by  friction  depended 
largely  upon  the   molecular   condition  of  the   surfaces. 
We  may  here  add  that  the  difference  of  potentials  pro- 
duced by  contact  of  dissimilar  substances   also   varies 
with  the  temperature  and  with  the  nature  of  the  medium 
(air,  vacuum,  etc.)  in  which  r  the  experiments  are  made. 
Doubtless  this  source  also  depends  upon  the  molecular 
conditions  of  dissimilar  substances  being  different ;  the 
particles   at    the   surfaces   being  of  different   sizes   and 
shapes,  and  vibrating  with  different  velocities  and  with 
different /orces.     There  are  (see  Art.  10)  good  reasons 
for  thinking  that  the  electricity  of  friction  is  really  due 
to  electricity  of  contact,  excited  at  successive  portions  of 
the  surfaces  as  they  are  moved  over  one  another.     But 
of  the  molecular  conditions  of  bodies  which  determine 
the  production  of  electricity  where  they  come  into  con- 
tact, little  or  nothing  is  yet  known. 


ELEMENTARY  LESSONS  ON        [CHAV.  n. 


CHAPTER    II 

MAGNETISM. 
LESSON  VI II. — Magnetic  Attraction  and  Repulsion. 

76.  Natural    Magnets    or     Loclestones.  —  The 
name    Magnet    (Rf<igne?    Lapis)    was    given    by    the 
ancients  lo  certain  hard  black  stones  found  in  various 
pails  of  the  world,  notably  at  Magnesia  in  Asia  Minor, 
which  possessed  the  property  of  attracting  to  them  small 
pieces  of  iron  or  steel.      This  magic  properly,  as  they 
deemed  it,  made  the  magnet-stone  famous  ;   but  it  was 
not  until  the  tenth  or  twelfth  century  that  such  stones 
were  discovered  lo  have  the  still  more  remaikable  pro- 
perty of  pointing  noith  and   south  when  hung  up  by 
a  thread.     This  properly  was  turned  to   advantage   in 
navigation,  and  from  that  time  the  magnet  received  the 
name    of    Lodestone l    (or    "  leading-slone").       The 
natural  magnet  or  lodestone  is  an  ore  of  iron,  known  to 
mineralogists    as  magnetite    and    having    the    chemical 
composition  Fe,  O4.     This  ore  is  found  in  quantities  in 
Sweden,  Spain,  Arkansas,  the  Isle  of  Elba,  and  other 
parts  of  the  world,  though  not  always  in  the  magnetic 
condition.      It  frequently  occurs  in  crystals  ;  the  usual 
form  being^the  regular  octahedron. 

77.  Artificial  Magnets.  —  If  a  piece  of  iron,   or, 
better  still,  a  piece  of  hard  steel,  be  rubbed  with  a  lode- 
stone,  it  will  be  found  lo  have  also  acquired  the  properties 
characteristic  of  the  magnet ;  it  will  attract  light  bits  of 

1  Tbe  common  spelling  /ou&cone  is  duo  to  in  isapprelieiuion. 


CHAP,  ii.]  ELECTRICITY  AND  MAG3STETISM. 


73 


iron,  and,  if  hung  up  by  a  thread  it  will  point  north 
and  south.  Figures 
40  and  41  represent 
a  natural  lodesfone 
and  an  artificial 
magnet  of  steel,  each 
of  which  has  been 
dipped  into  iron- 
filings  ;  the  filings 
are  attracted  and 

ii  .    f,  Figs.  40  and  41.. 

adhere  in  tufts. 

78.  Discoveries  of  Dr.  Gilbert. — This  was  all,  or 
nearly  all,  that  was  known  of  the  magnet  until  1600, 
when  Dr.  Gilbert  published  a  large  number  of  magnetic 
discoveries    in    his    famous    work  "  De  Magnete"     He 
observed  that  .the  attractive  power  of  a  magnet  appears 
to  reside  at  two  regions,  and  in  a  long-shaped  magnet 
these  regions,  or  poles,  are  usually  at  the  ends  (see  Figs. 
40  and '41).     The  portion  of  the  magnet  which  lies  be- 
tween the  two   poles   is   apparently  less  magnetic,  and 
does  not  attract  iron-filings  so  strongly ;  and  all  round 
the    magnet,  halfway   between    the    poles,   these   is   no 
attraction  at  all.    This  region  Gilbert  called  the  equator 
of  the  magnet,  and  the  imaginary  line  joining1  the  pojes 
he  termed  the  axia 

79.  Magnetic  Needle. — To  investigate  more  fully 
the  magnetic  forces  a  magnetic  needle  is  employed. 
This  consists  (Fig.  42)  of  a  light  needle  cut  out  of  steel, 
and  fitted  with  a  little  cap  of  brass,  glass,  or  agate,  by 
means  of  which  it  can  be  hung  upon  a  sharp  point,  so 
as  to  ttirn  \\iih  very  little  friction.      It  is  made  into  a 
magnet   by  being  rubbed   upon   a   magnet ;    and  when 
thus    magnetised  '  will    turn    into    the    north -and -south 
position,   or,  as  we   should   say,   will   set    itself   in    the 
".magnetic   meridian"  (Art.    136).      The   compass    sold 
by  opticians  consists  of  such  a  needle  balanced  above  a 
card  marked  v/ith  the  "  points  of  the  compass." 


74 


'ELEMENTARY  LESSONS  ON        [CHAP.  n. 


8O.  Magnetic  Attractions  and   Repulsions. — 

If  we  take  a  magnet 
(either  natural  or 
artificial)  in  our  hand 
and  present  the  two 
"  poles  "  of  it  succes- 
sively to  the  north  - 
pointing  end  of  a 
magnetic  needle,  we 
shall  observe  that 
one  pole  of  the  mag- 
net attracts  it,  while 
the  other  repels  it. 
(Fig.  43.)  If  .we 
repeat  the  experi- 
ment on  the  south- 
pointing  end  of  the 
magnetic  needle,  we 
shall  find  that  it  is 


Fig.  42. 


repelled  by  one  pole 
and  attracted  by 
the  other ;  and  that  the  same  pole  which  attracts  the 
north-pointing  end 
of  the  needle  re- 
pels the  south- 
pointing  end. 

If  we  try  a  simir 
lar  experiment  on 
the  magnetic 
needle,  using  for 
a  magnet  a  second 
magnetised  needle 
which  has  previ- 
ously been  sus- 
pended, and  which  has  its  north-pointing  end  marked 
•to  distinguish  it  from  the  south-pointing  end,  we  shall 
.discover  that  the  N.-pointing  pole  repels  the  N.-pointing 


Fig.  43- 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM.''  75 

pole,  and  that  the  S.-pointing  pole  repels  the  S.-pointing 
pole  ;  but  that  a  N.-pointing  pole  attracts  and  is  attracted 
by  a  S.-pointing  pole. 

81.  Two  kinds  of  Magnetic  Poles. — There  would 
therefore  appear  to  be  two  opposite  kinds  of  magnetism, 
or  at  any  rate  two  opposite  kinds  of  magnetic  poles, 
which  attract  or  repel  one  another  in  very  much  the 
same  fashion  as  the  two  opposite  kinds  of  electricity  do  ; 
and  one  of  these  kinds  of  magnetism  appears  to  have  a 
tendency  to  move  toward  the  north  and  the  other  to 
move  toward  the  south.  It  has  been  proposed  to  call 
these  two  kinds  of  magnetism  "  north-seeking  magnet- 
ism "  and  "  south-seeking  magnetism,"  but  for  our  pur- 
pose it  is  sufficient  to  distinguish  between  the  two  kinds 
of  poles.  In  common  parlance  the  poles  of  a  magnet 
are  called  the  "  North  Pole  "  and  "  South  Pole  "  respect- 
ively, and  it  is  usual  for  the  makers  of  magnets  to  mark 
the  N.-pointing  pole  with  a  letter  N.  It  is  therefore 
sometimes  called  the  "  marked  "  pole,  to  distinguish  it 
from  the  S.-pointing  or  "  unmarked  "  pole.  We  shall,  to 
avoid  any  doubt,1  call  that  pole  of  a  magnet  which 
would,  if  the  magnet  were  suspended,  tend  to  turn  to  the 

1  It  is  necessary  to  be  precise  on  this  point,  as  there  is  some  confusion  in 
the  existing  text-books.  The  cause  of  the  confusion  is  this  : — If  the  north- 
pointing  pole  of  a  needle  is  attracted  by  magnetism  residing  near  the  North 
Pole  of  the  earth,  the  law  of  attraction  (that  unlike  poles  attracf),  shows  us 
that  these  two  poles  are  really  magnetically  of  opposite  kinds.  Which  are 
we  then  to  call  north  magnetism  ?  That  which  is  at  the  N.  pole  of  the  earth? 
If  so,  we  must  say  that  the  N.-pointing  pole  of  the  needle  contains  south 
magnetism.  And  if  we  call  that  north  magnetism  which  points  to  the  north, 
then  we  must  suppose  the  magnetic  pole  at  the  north  pole  of  the  earth  to  have 
south  magnetism  in  it.  In  either  case  there  is  then  a  difficulty.  The  Chinese 
and  the  French  call  the  N.-pointing  pole  of  the  needle  a  south  pole,  and  the 
S. -pointing  pole  a  north  pole.  Sir  Wra.  Thomson  also  calls  the  N.-pointing 
pole  a  "True  South"  pole.  But  common  practice  gees  the  other  way,  and 
calls  the  N.-pointing  pole  of  a  magnet  its  "  North  "  pole.  For  experimental 
purposes  it  is  usual  to  paint  the  two  poles  of  a  magnet  of  different  colours, 
Uie  N. -seeking  pole  being  coloured  red  and  the  S. -seeking  pole  blue;  but 
here  agaiu,  strangely  enough,  authorities  differ,  for  in  the  collections  ol 
apparatus  at  the  Royal  Institution  and  Royal  School  of  Mines,  the  colour* 
arc  used  in  exartly  the  opposite  way  to  this,  which  is  due  to  Sir  G.  Airy  , 


76  ELEMENTARY  LESSONS  ON        [CHAP.  n. 

north,  the  "  North  -seeking"  pole,  and  the  other  the 
"  South-seeking  "  pole. 

We  may  therefore  sum  up  our  observations  in  the 
concise  statement :  Like  magnetic  poles  repel  one  another; 
unlike  poles  attract  one  another.  This  we  mav  call  the 
first  law  of  magnetism. 

82.  The  two  Poles  inseparable. — It  is  impossible 
to  obtain  a  magnet  with  only  one  pole.     If  we  magnetise 
a  piece  of  steel  wire,  or  watch  spring,  by  rubbing  it  with 
one  pole  of  a  magnet,  we  shall  find  that  still  it  has  two 
poles — one  N.-seeking,  the  other  S. -seeking.     And  if  we 
break   it  into  two   parts,  each   part  will  still  have  two 
poles  of  opposite  kinds. 

83.  Magnetic   Force. — The   force   with   which    a 
magnet  attracts  or  repels  another  magnet,  or  any  piece 
of  iron    or  steel,   we  shall  call  magnetic  forced      The 
force  exerted  by  a  magnet  upon  a  bit  of  iron  or  on  another 
magnet  is  not  the  same  at  all  distances,  the  force  being 
greater  when  the  magnet  is  nearer,  and  less  when  the 
magnet  is  farther  off.     In  fact  the  attraction  due  to  a 
magnet-pole  falls   off  inversely   as   the   square   of  the 
distance  from  the  pole.     (See  Art.  117.) 

Whenever  a  force  acts  thus  between  two  bodies,  it  acts 
on  both  of  them,  tending  to  move  both.     A  magnet  will 
attract  a  piece  of  iron,  and  a  piece  of  iron  will  attract  a 
magnet.       This    was    shown   by 
Sir    Isaac  Newton,  who  fixed  a 
magnet  upon  a  piece  of  cork  and 
floated    it    in    a  basin  of  water 
(Fig.  44),  and  found  that  it  moved 
across  the  basin  when  a  piece  of 
'iron  was  held  near.     A  compass 

needle  thus  floated  turns  round  and  points  north  and 
south  ;  but  it  does  not  rush  towards  the  north  as  a 
whole,  nor  towards  the  south.  The  reason  of  this  will 
be  explained  later,  in  Art.  117. 

1  See  footnote  on  "  Force,"  Art.  155. 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM.  77 

Gilbert  suggested  that  the  force  of  a  magnet  might  be 
measured  by  making  it  attract  a  piece  of  iron  hung  to 
one  arm  of  a  balance,  weights  being  placed  in  the  scale- 
pan  hanging  to  the  other  arm ;  and  he  found,  by  hang- 
ing the  'magnet  to  the  balance  and  placing  the  iron 
beneath  it,  that  the  effect  produced  was  the  same.  The 
action  and  reaction  are  then  equal  for  magnetic  forces. 

84.  Attraction   across   bodies.  —  If  a   sheet   of 
glass,  or  wood,  or  paper,  be  interposed  between  a  magnet 
and  the  piece  of  iron  or  steel  it  is  attracting,  it  will  still 
attract   it   as   if  nothing  were   interposed.      A  magnet 
sealed  up  in  a  glass  tube  stilj  acts  as  a  magnet.     Lucre- 
tius found  a  magnet  put  into  a  brass  vase  attracted  iron 
filings  through  the  brass.      Gilbert  surrounded  a  magnet 
by  a  ring  of  flames,  and  found  it  still  to  be  subject  to 
magnetic  attraction  from  without.     Across  v/ater,  vacuum, 
and  all  known  substances,  the  magnetic  forces  will' act ; 
with  the  single  exception,  however,  that  magnetic  force 
will  not  act  across  a  screen  of  iron  or  other  magnetic 
material.      If  a    small   magnet   is   suspended    inside   a 
hollow  ball  made  of  iron,  no  outside  magnet  will  affect  it 
A  hollow  shell  of  iron  will  therefore  act  as  a  magnetic 
cage,  and   screen   the    space    inside    it    from    magnetic 
influences. 

85.  Magnetic    Substances.  —  A    distinction    was 
drawn    by     Gilbert    between    magnets     and     magnetic 
substances.     A  magnet   attracts   only  at   its  poles,  and 
they  possess  opposite  properties.     But  a  lump  of  iron 
will  attract  either  pole  of  the  magnet,  no  matter  what 
part  of  the  lump  be  presented  to  the  magnet.      It  has  no 
distinguishable  fixed  "poles,"  and  no  magnetic  "equator." 
A  true  magnet  has  poles,  one  of  which  is  repelled  by  the 
pole  of  another  magnet. 

86.  Other  Magnetic  Metals. — Later  experimenters 
have  extended  the  list  of  substances  which  are  attracted 
by  a  magnet.      In  addition  to  iron  (and  steel)  the  follow^ 
ing  metals  are  recognised  as  magnetic  : — 


78  ELEMENTARY  LESSONS  ON        [CHAP,  II, 

Nickel.  Chromium. 

Cobalt.  Cerium. 

Manganese, 

and  a  few  others.  But  only  nickel  and  cobalt  are  at  all 
comparable  with  iron  and  steel  in  magnetic  power,  and 
even  they  are  very  far  inferior.  Other  bodies,  sundry  salts 
of  iron  and  other  metals,  paper,  porcelain,  and  oxygen 
gas,  are  also  very  feebly  attracted  by  a  powerful  magnet. 

87.  Diamagnetism. — A  number  of  bodies,  notably 
bismuth,  antimony,  phosphorus,  and  copper,  are  repelled 
from  the  poles  of  a  magnet.     Such  bodies    are  called 
diamagnetic  bodies  ;  a  fuller   account   of  them   will   be 
found  in  Lesson  XXVIII. 

88.  The    Earth    a    Magnet.  —  The    greatest    of 
Gilbert's  discoveries  was  that  of  the  inherent  magnetism 
of  the    earth.       The    earth    is   itself  a  great   magnet, 
whose  "  poles  "  coincide  nearly,  but  not  quite,  with  the 
geographical  north  and  south  poles,  and  therefore  it  causes 
a  freely-suspended  magnet  to  turn  into  a  north  and  south 
position.       The    subject    of    Terrestrial    Magnetism    is 
treated  of  in  Lesson  XII.     It  is  evident  from  the  first 
law  of  magnetism  that  the  magnetic  condition  of  the 
northern  regions  of  the  earth  must  be  the  opposite  to 
that  of  the  north-seeking  pole  of  a  magnetised  needle. 
Hence  arises  the  difficulty  alluded  to  on  page  75. 

89.  Magnetic    Induction.  —  Magnetism    may    be 
communicated  to  a  piece  of  iron,  without  actual  contact 
with  a  magnet.     If  a  short,  thin  unmagnetised  bar  of 
iron,  be  placed  near  some  iron  filings,  and  a  magnet  be 
brought  near  to   the  bar,  the  presence  of  the   magnet 
will  induce  magnetism  in  the  iron  bar,  and  it  will  now 
attract  the  iron  filings  (Fig.  45).      This  inductive  action 
is  very  similar  to  that  observed  in  Lesson  III.  to  take 
place  when  an  electrified  body  was  brought  near  a  non- 
electrified  one.     The  analogy,  indeed,  goes  farther  than 
this,  for  it  is  found  that  the  iron  bar  thus  magnetised  by 
induction  will  have  two  poles ;  the  pole  nearest  to  the 


.HAP.  ii.]    ELECTRICITY  AND  MAGNETISM. 


79 


>ole  of  the  inducing  magnet  being  of  the  opposite  kind, 
while  the  pole  at  the  farther  end  of  the  bar  is  of  the 
same  kind  as  the  inducing  pole.  Magnetism  can,  how- 
ever, only  be  induced  in  those  bodies  which  we  have 
enumerated  as  magnetic  bodies  ;  and  those  bodies  in 
which  a  magnetising  force  produces  a  high  degree  of 
magnetisation  are  said  to  possess  a  high  co-efficient 
of  magnetisation.  It  will  be  shown  presently  that 
magnetic  induction  takes  place  along  certain  direc- 
tions called  lines  of  magnetic  induction,  or  lines  of 
magnetic  force,  which  may  pass  either  through  iron 
and  other  magnetic  media,  or  through  air,  vacuum, 


Fig.  45. 

glass,  or  other  non-magnetic  media  :  and,  since  induction 
goes  on  most  freely  in  bodies  of  high  magnetic  suscepti- 
bility, those  lines  of  force  are  sometimes  (though  not 
too  accurately)  said  to  "  pass  by  preference  through 
magnetic  matter,"  or,  that  "  magnetic  matter  conducts 
*he  lines  of  force." 

<  Although  magnetic  induction  takes  place  at  a  distance 
across  an  intervening  layer  of  air,  glass,  or  vacuum, 
there  is  no  doubt  that  the  intervening  medium  is  directly 
concerned  in  the  transmission  of  the  magnetic  force, 
though  probably  the  true  medium  is  the  "  aether "  of 
space  surrounding  the  molecules  of  matter,  not  the 
molecules  themselves. 


So  ELEMENTARY  LESSONS  ON       [CHAP.  n. 

We  now  can  see  why  a  magnet  should  attract  a  not- 
previously-magnetised  piece  of  iron ;  it  first  magnetises 
it  by  induction  and  then  attracts  it :  for  the  nearest  end 
will  have  the  opposite  kind  of  magnetism  induced  in  it, 
and  will  be  attracted  with  a  force  exceeding  that  with 
which  the  more  distant  end  is  repelled.  But  induction 
precedes  attraction. 

OO.  Retention  of  Magnetisation. — Not  all  mag- 
netic substances  can  become  magnets  permanently. 
Lodestone,  steel,  and  nickel,  retain  permanently  the 
greater  part  of  the  magnetism  imparted  to  them.  Cast 
iron  and  many  impure  qualities  of  wrought  iron  also 
retain  magnetisrh  imperfectly. 
Pure  soft  iron  is, 'however,  only 
temporarily  ,  magnetic.  The 
following  experiment  illustrates 
the  matter:  —  Let  a  few  .pieces 
of  iron  rod,  or  a  few  soft  iron 
nails  be  taken.  If  one  of  these 
(see  Fig.  46)  be  placed  in  con- 
tact with  the  pole  of  a  perma- 
nent steel  magnet,  it  is  attracted 
to  it,  and  becomes  itself  a  tem- 
porary magnet.  Another  bit  of 

iron  may  then  be  hung  to  it,  and  another,  until  a  chain 
of  four  or  five  pieces  is  built  up.  But  if  the  steel 
magnet  be  removed  from  the  top  of  the  chain,  all  the 
rest  drop  off,  and  are  found  to  be  no  longer  magnetic. 
A  similar  chain  of  steel  needles  may  be  formed,  but 
they  will  retain  their  magnetism  permanently. 

It  will  be  found,  however,  that  a  steel  needle  is  more 
difficult  to  magnetise  than  an  iron  needle  of  the  same 
dimensions.  It  is  harder  to  get  the  magnetism  into 
steel  than  into  iron,  and  it  is  harder  to  get  the  magnetism 
out  of  steel  than  out  of  iron  ;  for  the  steel  retains  the 
magnetism,  once  put  into  it.  This  power  of  resisting 
magnetisation  or  demagnetisation,  is  sometimes  called 


CHAP.  «.]    ELECTRICITY  AND  MAGNETISM.  81 

coercive  force;  a  much  better  term,  due  to  Lament, 
is  retentivity.  The  retentivity  of  hard-tempered  steel 
is  great^  that  of  soft  wrought  iron  is  very  small.  The 
harder  the  steel,  the  greater  its  retentivity. 

191.  Theories  of  Magnetism. — The  student  will 
not  have  failed  to  observe  the  striking  analogies  between 
the  phenomena  of  attraction,  repulsion,  induction,  etc., 
of  magnetism  and  those  of  electricity.  Yet  the  two  sets 
of  phenomena  are  quite  distinct.  A  positively  electrified 
body  does  not  attract  either  the  North -pointing  or  the 
South -pointing  pole  of  the  magnet  as  such;  in  fact,  it 
attracts  either  pole'  quite  irrespective  of  its  magnetism, 
just  as  it  will  attract  any  other  body.  There  does 
exist,  indeed,  a  direct  relation  between  magnets  and 
currents  of  electricity,  as  will  be  later  explained.  There 
is  none  known,  however,  between  magnets  and  stationary 
charges  of  electricity. 

No  theory  as  to  the  nature  of  magnetism  has  yet 
been  placed  before  the  reader,  who  has  thus  been  told 
the  fundamental  facts  without  bias.  In  many  treatises 
it -is  the  fashion  to  speak  of  a  magnetic  fluid  or  fluids  j 
it  is,  however,  absolutely  certain  that  magnetism  is  not 
a  fluid,  whatever  else  it  may  be.  The  term,  which  is  a 
relic  of  bygone,  times,  is  only  tolerated  because,  under 
certain  circumstances,  magnetism  distributed  itself  in 
magnetic  bodies  in  the  same  manner  as  an  elastic 
fluid  would  .do.  Yet  the  reasons-  against  its  being  a 
fluid  are  even  more  conclusive  than  in  the  case  of 
electricity.  An  electrified  body  when  touched  against 
another  conductor,  electrifies  the  conductor  by  giving 
up  a  part  of  its  electricity  to  it.  But  a  magnet  when 
rubbed  upon  a  piece  of-  steel  magnetises  it  without 
giving  up  or  losing  any  of  its  own  magnetism.  A  fluid 
cannot  possibly  propagate  itself  indefinitely  without  loss. 
The  arguments  to  be  derived '  from  the  behaviour  of 
a  magnet  on  breaking,  and  from  other  experiments 
narrated  in  Lesson  X.,  are  even  stronger.  No  theory 

.0 


82  ELEMENTARY  LESSONS  ON        [CHAP.  «. 

of  magnetism  will  therefore  be  propounded  until  these 
facts  have  been  placed  before  the  student. 


LESSON  IX. — Methods  of  Making  Magnets. 

92.  Magnetisation   by   Single   Touch.  —  It  has 
been  so  far  assumed  that  bars  or  needles  of  steel  were 
to  be  magnetised  by  simply  touching  them,  or  stroking 
them  from  end  to  end  with  the  pole  of  a  permanent  magnet 
of  lodestone  or  steel.     In  this  case  the  last  touched  point 
of  the  bar  will  be  a  pole  of  opposite  kind  to  that  used 
to  touch  it ;  and  a  more  certain  effect  is  produced  if  one 
pole  of  the  magnet  be  rubbed  on  one  end  of  the  steel 
needle,  and  the  other  pole  upon  the  other  end.     There 
are,  however,  better  ways  of  magnetising  a  bar  or  needle. 

93.  Magnetisation  by  Divided  Touch. — In  this 
method  the  bar  to  be  magnetised  is  laid  down  hori- 
zontally ;  two  bar  magnets  are  then  placed  down  upon  it, 
their    opposite    poles    being    together.     They  are   then 
drawn  asunder  from  the  middle  of  the  bar  towards  its 


Fig.  47- 

ends,  and  back,  several  times.  The  bar  is  then  turned 
over,  and  the  operation  repeated,  taking  care  to  leave1  off 
at  the  middle  (see  Fig.  47).  The  process  is  more 
effectual  if  the  ends  of  the  bar  are  meantime  supported 
on  the  poles  of  other  bar  magnets,  the  poles  being  of 
the  same  names  as  those  of  the  two  magnets  above 
them  used  for  stroking  the  steel  bar. 

©4.  Magnetisation  by  Double  Touch. — Another 


CHAP.  IL]    ELECTRICITY  AND  MAGNETISM.  83 

method,  known  as  double  touch,  differs  slightly  from 
that  last  described.  A  piece  of  wood  or  cork  is  inter 
posed  between  the  ends  of  the  two  bar  magnets  employed, 
and  they  are  then  both  moved  backwards  and  forwards 
along  the  bar  that  is  to  be  magnetised.  By  none  of 
these  methods,  however,  can  a  steel  bar  be  magnetised 
beyond  a  certain  degree  of  intensity. 

95.  Laminated  Magnets. — It  is  found  that  long 
thin  steel  magnets  are  more  powerful  in  proportion  to 
their  weight  than  thicker  ones.     Hence  it  was  proposed 
by  Scoresby x  to  construct  compound  magnets,  consisting 
of  thin  laminae  of  steel  separately  magnetised,  and  after- 
wards  bound   together   in   bundles.     These   laminated 
magnets  are  more  powerful  than  simple  bars  of  steel. 

96.  Magnetisation  derived  from  the  Earth. — 
The  magnetism  of  the  earth  may  be  utilised,  where  no 
other  permanent  magnet  is  available,  to  magnetise  a  bar 
of  steel.     Gilbert  states  that  iron  bars  set  upright  for 
a  long  time,  acquire  magnetism  from  the  earth.     If  a 
steel  poker  be  held  in  the  magnetic  meridian,  with  the 
north  end  dipping  down,  and  in  this  position  be  struck 
with  a  wooden  mallet,  it  will  be  found  to  have  acquired 
magnetic  properties.    Wires  of  steel  subjected  to  torsion, 
while  in  the  magnetic  meridian,  are  also  found  to  be 
thereby  magnetised. 

97.  Magnetisation  after  Heating. — Gilbert  dis- 
covered also  that  if  a  bar  of  steel  be  heated  to  redness, 
and  cooled,  either  slowly  or  suddenly,  while  lying  in  the 
magnetic  meridian,  it  acquires  magnetic  polarity.     No 
such  property  is  acquired  if  it  is  cooled  while  lying  east- 
and-west.      It   has   been    proposed   to   make   powerful 
magnets  by  placing  hot  bars  of  steel  to  cool  between  the 
poles  of  very  powerful  electro-magnets ;  and  Carre"  has 
recently  produced  strong  magnets  of  iron  cast  in  moulds 
lying  in  an  intense  magnetic  field. 

1  A  similar  suggestion  was  made  by  Geuns  of  Venlo  in  1768.     Similar 
nagnets  have  been  constructed  recently  by  Jamin. 


84  ELEMENTARY  LESSONS  ON        [CHAF.  u 

98.  Magnetisation  by  Currents  of  Electricity. 
A  strong   current    of  electricity  carried  in  a  spiral  wire 
around  a  bar  of  iron  or  steel,  magnetises  it  more  power- 
fully than   in   any  of  the   preceding   operations.      In  the 
case  of  a  soft  iron  bar,  it  is  only  a  magnet   while  the 
current    continues    to    flow.       Such    a    combination    is 
termed  an  Electro-magnet ;   it   is  fully  described  in 
Lesson  XXVI.      Elias  of  Haarlem   proposed  to  mag- 
netise steel  bars  by  passing  them  through  a  wire   coiled 
up  into   a  ring  of  many  turns,  through  which  a  strong 
current  was  sent  by  a  voltaic  battery.     Tommasi  claims 
to  have  magnetised  steel  bars  by  passing  a  current  of 
hot  steam  round  them  in  a  spiral  tube :  but  the  matter 
needs  further  evidence. 

99.  Destruction  of  Magnetism. — A  steel  magnet 
loses  its   magnetism   partially  or   wholly  if  subjected   to 
rough  usage,  or  if  purposely  hit   or  knocked  about.      It 
also  loses  its  magnetism,  as  Gilbert   showed,  on   being 
raised  to  a  red-heat. 

100.  Effects  of  Heat  on  Magnetisation. — If  a 
permanent  steel  magnet  be  warmed  by  placing  it  in  hot 
or  boiling  water,  ils   strength  will   be   thereby  lessened, 
though    it    recovers    partially   on    cooling.-       Chilling    a 
magnet    increases   its   strength.       Cast    iron    ceases   to 
be  attracted  by  a  magnet  at  a  bright  red-heat,  or  at  a 
temperature  of  about  700°  C.     Cobalt  retains  its  mag- 
netism at  the  highest  temperatures.     Chromium  ceases 
to  be  magnetic  at  about   500°  C,  and  Nickel  at   350" 
C.      Manganese  exhibits  magnetic  attraction  only  when 
cooled  to  — 20°  C.     It  has  therefore  been  surmised  that 
other  metals  would  also  become  magnetic  if  cooled  to  a 
low  enough  temperature  ;  but  a  very  severe  cooling  to 
1 00°  below  zero  destroys  the  magnetism  of  steel  magnets. 
The  magnetic  metals  at  high  temperatures  do  not  be 
come  diamagnelic,  but  are  still  feebly  magnetic. 

101.  Forms   of   Magnets. —  Natural    Magnets   are 
usually   of  irregular   form,  though   they  are   sometimes 


CHAP,  it.)    ELECTRICITY  AND  MAGNETISM,  85 

reduced  to  regular  shapes  by  cutting  or  grinding. 
Formerly  it  was  the  fashion  to  mount  them  with  soft  iron 
cheeks  or  "  armatures  "  to  serve  as  pole-pieces. 

For  scientific  experiments  bar  magnets  of  hardened 
steel  are  commonly  used  ;  but  for  many  purposes  the 
horse-shoe  shape  is  preferred.  In  the  horse  shoe  magnet 
the  poles  are  bent  round  so  as  to  approach  one  another, 
the  advantage  here  being  that  so  both  poles  can  attract 
one  piece  of  ir<5n.  The  "  armature,"  or  "  keeper,"  as 
the  piece  of  soft  iron  placed  across  the  poles  is  named,  is 
itself  rendered  a  magnet  by  induction  when  placed  across 
jhe  poles  ;  hence,  when  both  poles  magnetise  it,  the  force 
with  which  it  is  attracted  to  the  magnet  is  the  greater. 

102.  Magnetic  Saturation.— A  magnet  to  which 
as  powerful  a  degree  of  magnetisation  as  it  can  attain  to 
has  been  given  is  said  to  be  "saturated."  Many  of 
the  methods  of  magnetisation  described  will  excite  in  a 
magnet  a  higher  degree  of  magnetism  than  it  is  able  to 
retain  permanently.  A  recently  magnetised  magnet  will 
occasionally  appear  to  be  supersaturated^  even  after 
the  application  of  the  magnetising  force  has  ceased. 
Thus  a  horse-shoe-shaped  steel  magnet  will  support  a 
greater  weight  immediately  after  being  magnetised  than 
it  will  do  after  its  armature  has  been  once  removed  from 
its  poles.  Even  soft  iron  after  being  magnetised  retains 
a  small  amount  of  magnetism  when  its  temporary  mag- 
netism has  disappeared.  This  small  remaining  magnetic 
charge  is  spoken  of  as  residual  magnetism. 

Strength  of  a  Magnet.—  The  "  strength "  of  a 
magnet  is  not  the  same  thing  as  its  "  lifting-power."  The 
"  strength  "  of  a  magnet  is  the  "  strength  "  of  its  poles. 
The  "  strength  "  of  a  magnet  pole  must  be  measured  by 
the  magnetic  force  which  it  exerts.  Thus,  suppose  there 
are  two  magnets,  A  and  B,  whose  strengths  we  compare 
by  making  them  each  act  upon  the  N.  pole  of  a  third 
magnet  C.  If  the  N  pole  of  A  repels  C  with  twice  as 
much  force  as  that  with  which  the  N.  pole  of  B  placed 


86  ELEMENTARY  LESSONS  ON        [CHAP,  il. 

at  the  same  distance  would  repel  C,  then  we  should  say 
that  the  "  strength  "  of  A  was  twice  that  of  B.  Another 
way  of  putting  the  matter  is  to  say  that  the  "  strength  " 
of  a  pole  is  the  amount  of  free  magnetism  at  that  pole. 
By  adopting  the  unit  of  strength  of  magnet  poles  as 
defined  in  Art.  125,  we  can  express  the  strength  of  any 
pole  in  numbers  as  so  many  "  units  "  of  strength. 

103.  Lifting  Power.  —  The  lifting  power  of  a  magnet 
(also  called  its  '•'•portative  force  ")  depends  both  upon 
the  form  of  the  magnet  and  on  its  magnetic  strength.  A 
horse-shoe  magnet  will  lift  a  load  three  or  four  times  as 
great  as  a  bar  magnet  of  the  same  weight  will  lift.  The 
lifting  power  is  greater  if  the  area  of  contact  between  the 
poles  and  the  armature  is  increased.  Also  the  lifting 
power  of  a  magnet  grows  in  a  very  curious  and  unex- 
plained way  by  gradually  increasing  the  load  on  its 
armature  day  by  day  until  it  bears  a  load  which  at  the 
outset  it  could  not  have  done.  Nevertheless,  if  the  load 
is  so  ir  Creased  that  the  armature  is  torn  off,  the  power 
of  the  magnet  falls  at  once  to  its  original  value.  The 
attraction  between  a  powerful  electro-magnet  and  its 
armature  may  amount  to  200  Ibs.  per  square  inch,  or 
14,000  grammes  per  square  centimetre.  Small  magnets 
lift  a  greater  load  in  proportion  te  their  own  weight  than 
large  ones.1  A  good  steel  horse-shoe  magnet  weighing 
itself  one  pound  ought  to  lift  twenty  pounds'  weight. 
Sir  Isaac  Newton  is  said  to  have  possessed  a  Iktle  lode- 
stone  mounted  in  a  signet  ring  which  would  lift  a  piece 
of  iron  200  times  its  own  weight. 

1  Bernoulli  gave  the  following  rule  for  finding  the  lifting-power  /  of  a 
magnet  whose  weight  was  in  :  — 


where  a  is  a.  constant  depending  on  the  goodness  of  the  steel  and  the  method 
of  -magnetising  it.  In  the  best  steel  magnets  made  at  Haarlem  by  V. 
Wetteren  this  coefficient  was  from  19*5  to  23.  In  Breguet's  magnets,  made 
from  Allevard  steel,  the.  value  is  equally  high. 


CHAP,  ii.]    ELECTRIC ITY  AND  MAGNETISM.  87 

LESSON  X. — Distribution  of  Magnetism. 

104.  Normal  Distribution. — In  an  ordinary  bar 
magnet  the  poles  are  not  quite  at  the  ends  of  the  bar, 
but  a  little  way  from  it ;  and  it  can  be  shown  that  this  is 
a  result  of  the  way  in  which  the  magnetism  is  distributed 
in  the  bar.     A  very  long,  thin,  uniformly  magnetised  bar 
has  its  poles  at  the  ends  ;  but  in  ordinary  thick  magnet^ 
the  "  pole "  occupies  a  considerable  region,  the  "  free 
magnetism  "  falling  off  gradually  from  the,  ends  of  the 
bar.     In  each  region,  however,  a  point  can  be  determined 
at  which  the  resultant  magnetic  forces  act,  and  which 
may  for  most  purposes  be  considered  as  the  pole.      In 
certain  cases  of  irregular  magnetisation  it  is  possible  to 
have  one   or  more   poles  between   those   at   the  ends. 
Such  poles  are  called  consequent  poles  (see  Fig.  51). 

105.  Magnetic   Field.  —  The    space   all    round   a 
magnet  pervaded  by  the  magnetic  forces  is  termed  the 
"field"  of  that  magnet.      It  is  most  intense  near  the  pole 
of  the  magnet,  and  is  weaker  and  weaker  at  greater  dis- 
tances away  from  it.     At  ever)*  point  in  a  magnetic  field 
tlie  force  has  a  particular  strength,  and  the  magnetic 
induction  acts  in  a  particular  direction  or  line.      In  the 
horse-shoe  magnet  the  field  is  most  intense  between  the 
two  poles,  and  the  lines  of  magnetic  induction  are  curves 
which  pass  from  one  pole  to  the  other  across  the  field. 
A  practical  way  of  investigating  the  distribution  of  the 
lines  of  induction  in  a  field  is  given  in  Art.  108,  under  the 
title  "  Magnetic  Figures."    When  the  armature  is  placed 
upon  the  poles  of  a  horse-shoe  magnet,  the  force  of  the 
magnet  on  all  the  external  regions  is  weakened,  for  the 
induction  now  goes  on  through  the  iron  of  the  keeper, 
not   through  the  surrounding  space.     In  fact  a  closed 
system  of  magnets — such  as  that  made  by  placing  four 
bar  magnets  along  the  sides  of  a  square,  the  N.  pole  of 
one  touching  the  S.  pole  of  the  next — has  no  external 
field  of  force.     A  ring  of  steel  may  thus  be  magnetised 


88 


ELEMENTARY  LESSONS  ON        [CHAP.  n. 


so  as  to  have  neither  external  field  nor  poles ;  or  rather 
any  point  in  it  may  be  regarded  as  a  N.  pole  and  a  S. 
pole,  so  close  together  that  they  neutralise  one  another's 
forces. 

That  poles  of  opposite  name  do  neutralise  one  another 
may  be  shown  by  the  well-known  experiment  of  hanging 
a  small  object — a  steel  ring  or  a  key — to  the  N.  pole  of 
a  bar  magnet.  If  now  the  S.  pole  of  another  bar  magnet 
be  made  to  touch  the  first  the  two  poles  will  neutralise 
each  other's  actions,  and  the  ring  or  key  will  drop  down. 

1O6.  Breaking  a  Magnet. — We  have  already  stated 
that  when  a  magnet  is  broken  into  two  or  more  parts,  each 
is  a  complete  .magnet,  possessing  poles,  and  each  is 
nearly  as  strongly  magnetised  as  the  original  magnet. 
Fig.  48  shows  this.  If  the  broken  parts  be  closely  joined 


these  adjacent  poles  neutralise  one  anomer  and  disappear, 
leaving  only  the  poles  at  the  ends  .as  before.  <  If  a  magnet 
be  ground  to  powder  each  fragment  will  still  act  as  a 
little  magnet  and  exhibit  polarity.  A  magnet  may  there- 
fore be  regarded  as  composed  of  many  little  magnets 


N 


S'N' 


n         s 

n       f, 

n      s 

n     s 

•n       s 

n      s 

7',         S 

n      s 

n        s 

n       s 

n       s 

n      s 

n      x 

w      s 

n      s 

n      s 

n        s 

n       F. 

n      s 

n      s 

n       s 

n      s 

n      s 

n      s 

n        s 

n      _$_ 

n      s 

n      K 

«       s 

n      s 

n      s 

n      s 

N 

S'tf                             S 

Fig.  49. 

put  together,  so  that  their  like  poles  all  face  one  way. 
Such  an  arrangement  is  indicated  in  Fig.  49,  from  which 
it  will  be  seen  that  if  the  magnet  be  broken  asunder  across 
any  part,  one  face  of  the  fracture  will  present  only  N= 


CHAP,  ii.]   ELECTRICITY  AND  MAGNETISM.  89 

poles,  the  other  only  S.  poles.     This  would  be  true  no 
matter  how  small  the  individual  particles. 

If  the  intrinsic  magnetisation  of  the  steel  at  every 
part  of  a  magnet  were  equal,  the  free  poles  would  be 
found  only  at  the  ends  ;  but  the  fact  that  the  free  mag- 
netism is  not  at  the  ends  merely,  but  diminishes  from 
the  ends  towards  the  middle,  shows  that  the  intensity  of 
the  intrinsic  magnetisation  must  be  less  towards  and  at 
the  ends  than  it  is  at  the  middle  of  the  bar. 

107.  Lamellar     Distribution    of    Magnetism. 
Magnetic    Shells.  —  Up   to    this    point   the    ordinary 
distribution  of  magnetism  along  a  bar  has  been  the  only 
distribution    considered.      But    it    is    possible    to    have 
magnetism   distributed   over  a  thin   sheet    so    that  the 
whole  of  one  face  of  the  sheet  shall  have  one  kind  of 
magnetism,  and  the  other  face  the  other  kind  of  magnet- 
ism.     If  an   immense  number  of  little  magnets  were 
placed  together  side  by  side,  like  the  cells  in  a  honey 
comb,  all  with  their  N. -seeking  ends  upwards,  and  S.- 
seeking  ends  downwards,  the  whole  of  one  face  of  the 
slab  would  be  one  large  flat  N. -seeking  pole,  and  the 
other  face  S.-seeking.     Such  a  distribution  a^s  this  over  a 
surface  or  sheet  is  termed  a  lamellar  distribution,  to 
distinguish  it  from  the  ordinary  distribution  along  a  line 
or  bar,  which  is  termed,  for  distinction,  the  solenoidal 
distribution.     A  lamellarly  magnetised  magnet  is  some- 
times spoken  of  as  a  magnetic  shell.     The  properties 
of  magnetic  shells  are  extremely  important  on  account  of 
their  analogy  with  those  of  closed  voltaic  circuits. 

108.  Magnetic  Figures. — Gilbert  showed1  that  if 
a  sheet  of  paper  or  card  be  placed  over  a  magnet,  and 
iron-filings  are  dusted  over  the  paper,  they  settle  down 
in  curving  lines,  forming  a  magnetic  figure,  the  general 
form  of  which  is  shown  in  Fig.  50.     The  filings  should 
be  fine,  and  silted  through  a  bit  of  muslin ;  to  facilitate 
their  settling  in  the  lines,  the  sheet  of  paper  should  be 

1  ^he  magnetic  figures  were  known  to  Lucretius. 


go  ELEMENTARY  LESSONS  ON        [CHAP.  II. 

lightly  tapped*  The  figures  thus  obtained  can  be  fixed 
permanently  by  several  processes.  The  best  of  these 
consists  in  employing  a  sheet  of  glass  which  has  been 
previously  gummed  and  dried,  instead  of  the  sheet  of 
paper ;  after  this  has  been  placed  above  the  magnet  the 
filings  are  sifted  evenly  over  the  surface,  and  then  the 
glass  is  tapped  ;  then  a  jet  of  steam  is  caused  to  play 
gently  above  the  sheet,  softening  the  surface  of  the  gum, 
which,  as  it  hardens,  fixes  the  filings  in  their  places.  In- 


Fig.  50. 

spection  of  the  figure  will  show  that  the  lines  diverge 
nearly  radially  from  each  pole,  and  curve  round  to  meet 
these  from  the  opposite  pole.  Faraday,  who  made  a 
great  use  of  this  method  of  investigating  the  distribution 
of  magnetism  in  various  "  fields,"  gave  to  the  lines  the 
name  of  lines  of  force.  They  represent,  as  shown 
by  the  action  on  little  magnetic  particles  which  set  them- 
selves thus  in  obedience  to  the  attractions  and  repulsions 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM.  91 

in  the  field,  the  resultant  direction  of  the  forces  at  every 
point ;  for  each  particle  tends  to  assume  the  direction  of 
the  magnetic  induction  due  to  the  simultaneous  action  of 
both  poles  :  hence  they  may  be  taken  to  represent  the 
lines  of  magnetic  induction.^-  Faraday  pointed  out 
that  these  "  lines  of  force  "  map  out  the  magnetic  field, 
showing  by  their  position  the  direction  of  the  magnetic 
force,  and  by  their  number  its  intensity.  If  a  small  N.- 
seeking  pole  could  be  obtained  alone,  and  put  dov/n  on 
any  one  of  these  lines  of  force,  it  would  tend  to  move 
along  that  line  from  N.  to  S.  ;  a  single  S.-seeking  pole 
would  tend  to  move  along  the  line  in  an  opposite  direc- 
tion. Faraday  also  assigned  to  these  lines  of  force 
certain  physical  properties  (which  are,  however,  only 
true  of  them  in  a  secondary  sense),  viz.,  that  they  tend 
to  shorten  themselves  from  end  to  end,  and  that  they 
repel  one  another  as  they  lie  side  by  side.  The  modern 
view,  which  holds  that  magnetism  results  from  certain 
properties  of  the  "  eether "  of  space,  is  content  to  say 
that  in  every  magnetic  field  there  are  certain  stresses, 
which  produce  a  tension  along  the  lines  of  force,  and  a 
pressure  across  them. 

109.  This  method  may  be  applied  to  ascertain  the 
presence  of  "  consequent  poles "  in  a   bar  of  steel,  the 
figure   obtained    resembling   that   depicted  in    Fig.    51. 
Such  a  state  of  things  is  produced  when  a  strip  of  very 
hard  steel  is  purposely  irregularly  magnetised  by  touching 
it  with  strong  magnets  at  certain  points.     A  strip  thus 
magnetised  virtually  consists  of  several  magnets  put  end 
to  end,  but  in  reverse  directions,  N.-S.,  S.-N.,  etc. 

110.  The  forces  producing  attraction  between  unlike 
poles,  and  repulsion  between  like  poles,  are  beautifully 
illustrated  by  the  magnetic  figures  obtained  in  the  fields 
between  the  poles  in  the  two  cases,  as  given  in  Figs. 

1  Or  rather  the  component  part  of  the  magnetic  induction  resolved  into 
the  plane  of  the  figure  ;  which  is  net  quite  the  same  thing,  for  above  the 
poles  the  tilings  stand  up  nearly  vertically  to  this  plane. 


92  ELEMT.NTARY  LESSONS  ON        [CHAP.  n. 


52  and  53.  In  Fig.  52  the  poles  are  of  opposite  kinds, 
and  the  lines  of  force  curve  across  out  of  one  pole  into 
the  other;  while  in  Fig.  53,  which  represents  the  action 


Fig.  SL 

of  two  similar  poles,  the  lines  of  force  curve  away  as  if 
repelling  one  another,  and  turn  aside  at  right  angles. 
Musschenbroek  first  pointed  out  the  essential  difference 
between  these  two  figures. 


Fig.  52-  F;s-  53- 

111.  Magnetic  Writing. — Another  kind  of  magnetic 
figures  was  discovered  by  De  Haldat.  who  wrote  with  the 
pole  of  a  magnet  upon  a  thin  steel  plate  (such  as  a  saw- 
blade),  and  then  sprinkled  filings  over  it.  The  writing, 
which  is  quite  invisible  in  itself,  comes  out  in  the  lines 
of  filings  that  stick  to  the  magnetised  parts  ;  this  magic 
writing  will  continue  in  a  steel  plate  many  months.  The 
author  of  these  Lebbons  has  produced  similar  figures  in 


CHAP.  «.]    ELECTRICITY  AND  MAGNETISM.  93 

iron  filings  by  writing  upon  a  steel  plate  with  the  wires 
coming  from  a  powerful  voltaic  battery. 

112.  Surface  Magnetisation. — In  many  cases  the 
magnetism  imparted  to  magnets  is  confined  chiefly  to 
the  outer  layers  of  steel.     If  a  steel  magnet  be  put  into 
acid  so  that  the  outer  layers  are  dissolved  away,  it  is 
found  that  it  has  lost  its  magnetism  when  only  a  thin 
film  has  been  thus  removed.     Magnets  which  have  been 
magnetised    very  thoroughly,    however,     exhibit    some 
magnetism   in  the  interior.     A  hollow  steel  tube  when 
magnetised  is  nearly  as  strong  a  magnet  as  a  solid  rod 
of  the  same  size.      If  a  bundle  of  steel  plates  are  mag- 
netised while  bound  together,  it  will  be  found  that  only 
the  outer  ones  are  strongly  magnetised.     The  inner  ones 
may  even  exhibit  a  reversed  magnetisation. 

113.  Mechanical   effects    of    Magnetisation. — 
When  a  steel  or  iron  bar  is  powerfully  magnetised   it 
grows  a  little  longer  than  before ;  and,  since  its  volume 
is  the  same  as  before,  it  at  the  same  time  contracts  in 
thickness.    Joule  found  an  iron  bar  to  increase  by  7  a  0*0 o  o 
of  its  length  when  magnetised  to  its  maximum.     This 
phenomenon  is  believed  to  be  due  to  the  magnetisation 
of  the  individual  particles,  which,  when  magnetised,  tend 
to  set  themselves  parallel  to  the  length  of  the  bar.     This 
supposition  is  confirmed  by  the  observation  of  Page,  that 
at  the  moment  when  a  bar  is  magnetised  or  demagnetised, 
a  faint  metallic  clink  is  heard  in  the  bar.     Sir  W.  Grove 
showed  that   when    a    tube    containing  water  rendered 
muddy  by  stirring  up  in  it  finely  divided  magnetic  oxide 
of  iron  was  magnetised,  the  liquid  became  clearer  in  the 
direction  of  magnetisation,  the  particles  apparently  setting 
themselves  end-on,  and  allowing  more  light  to  pass  be- 
tween them.     A  twisted  iron  wire  tends  to  untwist  itself 
when  magnetised.    A  piece  of  iron,  when  powerfully  mag- 
netised and  demagnetised  in  rapid  succession,  grows  hot, 
as  if  magnetisation  were  accompanied  by  internal  friction. 

114.  Action  of  Magnetism  on  Light. — Faraday 


94  ELEMENTARY  LESSONS  ON        [CHAP.  n. 

discovered  that  a  ray  of  polarised  light  passing  through  certain 
substances  in  a  powerful  magnetic  field  has  the  direction  of  its 
vibrations  changed.  This  phenomenon,  which  is  sometimes 
called  "The  Magnetisation  of  Light,"  is  better  described  as 
"  The  Rotation  of  the  Plane  of  Polarisation  of  Light  by  Mag- 
netism."  The  amount  of  rotation  differs  in  different  media, 
and  varies  with  the  magnetising  force.  More  recently  Kerr 
has  shown  that  a  ray  of  polarised  light  is  also  rotated  by  re- 
flection at  the  end  or  side  of  a  powerful  magnet.  Further 
mention  is  made  of  these  discoveries  in  the  Chapter  on  Electro- 
optics,  Lesson  XXXV. 

115.  Physical  Theory  of  Magnetism. — All  these  various 
phenomena  point  to  a  theory  of  magnetism  very  different  from 
the  old  notion  of  fluids.  It  appears  that  every  particle  of  a 
magnet  is  itself  a  magnet,  and  that  the  magnet  only  becomes  a 
magnet  as  a  whole  by  the  particles  being  so  turned  as  to  point 
one  way.  This  conclusion  is  supported  by  the  observation  that 
if  a  glass  tube  full  of  iron  filings  is  magnetised,  the  filings  can 
be  seen  to  set  themselves  endways,  and  that,  when  thus  once 
set,  they  act  as  a  magnet  until  shaken  up.  It  appears  to  be 
harder  to  turn  the  individual  molecules  of  solid  steel,  but.  when 
once  so  set,  they  remain  end -on  unless  violently  struck  or 
heated.  It  follows  from  this  theory  that  when  all  the  particles 
were  turned  end-on  the  limits  of  possible  magnetisation  would 
have  been  attained.  Some  careful  experiments  of  Beetz  on  iron 
deposited  by  electrolysis  entirely  confirm  this  conclusion,  and 
add  weight  to  the  theory.  The  optical  phenomena  led  Clerk 
Maxwell  to  the  further  conclusion  that  these  longitvdinally-set 
molecules  are  rotating  round  their  long  axes,  and  that  in  the 
"  sether  "  of  space  there  is  alro  a  vortical  motion  along  the  lines 
of  magnetic  induction  ;  this  motion,  if  occurring  in  a  perfect 
medium  (as  the  "  aether  "  may  be  considered),  producing  tensions 
along  the  lines  and  pressures  at  right  angles  to  them,  would 
afford  a  satisfactory  explanation  of  the  magnetic  attractions  and 
repulsions  which  apparently  act  across  empty  space.  Hughes 
has  lately  shown  that  the  magnetism  of  iron  and  steel  is  inti'nateiy 
connected  with  the  molecular  rigidity  of  the  material.  His 
researches  -vuth  the  "induction  balance"  (Art.  438)  and  "mag- 
netic balance  "  (Art.  439)  tend  to  prove  xhat  each  molecule  of 
a  magnetic  metal  has  an  absolutely  constant  inherent  magnetic 
polarity ;  and  that  v/hen  a  piece  of  iron  or  steel  is  apparently 
neutral,  its  molecules  are  internally  arranged  so  ES  to  Fati-vfy 
each  other's  polarity,  forming  closed  magnetic  circuits  amongst 


CHAP,  ii.]     ELECTRTCITY  AND  MAGNETISM.  f         95 

themselves.     On  this  view  magnetising  a  piece  of  iron  simply 
causes  the  molecules  to  rotate  into  new  and  symmetrical  positions. 

LESSON  XI. — Laws  of  Magnetic  Force. 

116.  Laws  of  Magnetic  Force. 

FIRST  LAW.  —  Like  magnetic  poles  repel  one 
another;  unlike  magnetic  poles  attract  one 
another. 

SECOND  LAW. —  The  force  exerted  between  two 
magnetic  poles  is  proportional  to  the  product 
of  their  strengths^  and  is  inversely  propor- 
tional to  the  square  of  the  distance  between 
them. 

117.  The  Law  of  Inverse  Squares. — The  second 
of  the  above  laws  is  commonly  known  as  the  law  of 
inverse  squares.     The  similar  law  of  electrical  attrac- 
tion has  already  been  explained  and   illustrated  (Art 
1 6).     This  law  furnishes  the  explanation  of  a  fact  men- 
tioned in  an  earlier  Lesson,  Art.  77,  that  small  pieces 
of  iron  are  drawn  bodily  up  to  a  magnet  pole.     If  a 
small  piece  of  iron  wire,  a  b  (Fig.  54),  be  suspended  by 
a  thread,  and  the 

N.- pointing  pole 
A  of  a  magnet  be 
brought  near  it, 
the  iron  is  thereby 
inductively  mag- 
netised ;  it  turns 

round  and  points  Fi 

towards  the  mag- 
net pole,  setting  itself  as  nearly  as  possible  along  a  line 
of  force,  its  near  end  b  becoming  a  S. -seeking  pole,  and 
its  further  end  a  becoming  a  N. -seeking  pole.  Now  the 
pole  b  will^be  attracted  and  the  pole  a  will  be  repelled. 
But  these  two  forces  do  not  exactly  equal  one  another, 
since  the  distances  are  unequal  The  repulsion  will 


96  ELEMENTARY  LESSONS  ON        [CHAP,  a 

(by  the  law  of  inverse  squares)  be  proportional  to 
r^r-^j ;  and  the  attraction  will  be  proportional  to  rr-rra- 

Hence  the  bit  of  iron  a  b  will  experience  a  pair  of  forces, 
turning  it  into  a  certain  direction,  and  also  a  total  force 
drawing  it  bodily  toward  A.  Only  those  bodies  are 
attracted  by  magnets  in  which  magnetism  can  thus  be 
induced;  and  they  are  attracted  only  because  of  the 
magnetism  induced  in  them. 

We  mentioned,  Art.  83,  that  a  magnet  needle  floating 
freely  on  a  bit  of  cork  on  the  surface  of  a  liquid,  is  acted 
upon  by  forces  that  give  it  a  certain  direction,  but  that, 
unlike  the  last  case,  it  does  not  tend  to  rush  as  a  whole 
either  to  the  north  or  to  the  south.  It  experiences  a 
rotation,  because  the  attraction  and  repulsion  of  the 
magnetic  poles  of  the  earth  act  in  a  certain  direction ; 
but  since  the  magnetic  poles  of  the  earth  are  at  a  dis- 
tance enormously  great  as  compared  with  the  length 
from  one  pole  of  the  floating  magnet  to  the  other,  we 
may  say  that,  for  all  practical  purposes,  the  poles  of  the 
magnet  are  at  the  same  distance  from  the  N.  pole  of  the 
earth.  The  attracting  force  on  the  N. -pointing  pole  of 
the  needle  is  therefore  practically  no  greater  than  the 
repelling  force  acting  011  the  S.- pointing  pole,  hence 
there  is  no  motion  of  translation  given  to  the  floating 
needle  as  a  whole. 

118.  Measurement  of  Magnetic  Forces. — The 
truth  of  the  law  of  inverse  squares  can  be  demonstrated 
by  measuring  the  attraction  between  two  magnet  poles 
at  known  distances.  But  this  implies  that  we  have 
some  means  of  measuring  accurately  the  amount  of  the 
magnetic  forces  of  attraction  or  repulsion.  Magnetic 
force  may  be  measured  in  any  one  of  the  four  following 
ways:  (i)  by  balancing  it  against  the  torsion  of  an 
elastic  thread ;  (2)  by  observing  the  time  of  s?/ing  of 
a  magnetic  needle  oscillating  under  the  influence  of  the 
force  ;  (3)  by  observing  the  deflection  it  produces  upon  a 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM. 


97 


magnetic  needle  which  is  already  attracted  into  a  different 
direction  by  a  force  of  known  intensity  ;  (4)  by  balanc- 
ing it  against  the  force  of  gravity  as  brought  into  play 
in  attempting  to  deflect  a  magnet  hung  by  two  parallel 
strings  (called  the  bifilar  suspension),  for  these  strings 
cannot  be  twisted  out  of  their  parallel  position  without 
raising  th'e  centre  of  gravity  of  the  magnet.  The  first 
three  of  these  methods  must  be  further  explained. 

119.  The  Torsion  Balance. — Coulomb  also  applied 
the  Torsion  Balance  to  the  measurement  of  magnetic 


55- 


/orces.  The  main  principles  of  this  instrument  (as  used 
to  measure  electrostatic  forces  of  repulsion)  were  de- 
scribed on  p.  15.  Fig.  55  shows  how  it  is  arranged  for 

H 


98  ELEMENTARY  LESSONS  ON        [CHAP,  n 

measuring  magnetic  repulsions.  By  means  of  the 
torsion  balance  we  may  prove  the  law  of  inverse  squares. 
We  may  also,  assuming  this  law  proved,  employ  the 
balance  to  measure  the  strengths  of  magnet  poles  by 
measuring  the  forces  they  exert  at  known  distances. 

To  prove  the  law  of  inverse  squares,  Coulomb  made 
the  following  experiment : — The  instrument  was  first 
adjusted  so  that  a  magnetic  needle,  hung  in  a  copper 
stirrup  to  the  fine  silver  thread,  lay  in  the  magnetic 
meridian  without  the  wire  being  twisted.  This  was  done 
by  first  putting  in  the  magnet  and  adjusting  roughly, 
then  replacing  it  by  a  copper  bar  of  equal  weight,  and 
once  more  adjusting,  thus  diminishing  the  error  by 
repeated  trials.  The  next  step  was  to  ascertain  through 
what  number  of  degrees  the  torsion -head  at  the  top 
of  the  thread  must  be  twisted  in  order  to  drag  the 
needle  i°  out  of  the  magnetic  meridian.  Tn  the  par- 
ticular experiment  cited  it  was  found  that  35°  of  torsion 
corresponded  to  the  i°  of  deviation  of  the  magnet  ;  then 
a  magnet  was  introduced,  that  pole  being  downwards 
which  repelled  the  pole  of  the  suspended  needle.  It  was 
found  (in  this  particular  experiment)  to  repel  the  pole  of 
the  needle  through  24°.  From  the  preliminary  trial  we 
know  that  this  directive  force  corresponds  to  24°  x  35° 
of  the  torsion -head,  and  to  this  we  must  add  the 
actual  torsion  on  the  wire,  viz.,  the  24°,  making  a  total 
of  864°,  which  we  will  call  the  "  torsion  equivalent "  of 
the  repelling  force  when  the  poles  are  thus  24°  apart. 
Finally,  the  torsion-head  was  turned  round  so  as  to 
twist  the  suspended  magnet  round,  and  force  it  nearer 
to  the  fixed  pole,  until  the  distance  between  the  repelling 
poles  was  reduced  to  half  what  it  was  at  first  It  was 
found  that  the  torsion -head  had  to  be  turned  round  8 
complete  rotations  to  bring  the  poles  to  12°  apart 
These  8  rotations  were  an  actual  twist  of  8°  x  360°,  01 
2880°.  But  the  bottom  of  the  torsion  thread  was  still 
twisted  12°  as  compared  with  the  top,  the  force  pro 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM.  99 

during  this  twisi  corresponding  to  12  x  35  (or  420°)  of 
torsion;  and  to  these  the  actual  torsion  of  12°  must  be 
added,  making  a  total  of  2880°  +  420°  +  12"  =  3312 
The  result  then  of  halving  the  distance  between  the 
magnet  poles  was  to  increase  the  force  fourfold^  for 
3312  is  very  nearly  four  times  864.  Had  the  distance 
between  the  poles  been  reduced  to  one-third  the  force 
would  have  been  nine  times  as  great. 

120.  Method  of  Oscillations.1 — If  a  magnet  sus- 
pended  by  a  fine  thread,  or  poised   upon  a  point,  be 
pushed  aside  from  its  position  of  rest,  it   will  vibrate 
backwards  and  forwards,  performing  oscillations  which, 
Although    they   gradually   decrease    in    amplitude,    are 
executed  in  very  nearly  equal  times.     In  fact,  they  follow 
a  law  similar  to  that  of  the  oscillations  executed  by  a  pen- 
dulum  swinging  under  the  influence  of  gravity.     The  law 
of  pendular  vibrations  is,  that  th&  square  of  the  number 
of  oscillations  executed  in  a  given  time  is  proportional  to 
the  force.     Hence  we  can  measure  magnetic  forces  by 
counting  the  oscillations  made  in  a  minute  by  a  magnet. 
It  must  be  remembered,  however,  that  the  actual  number 
of  oscillations  made  by  any  given  magnet  will  depend 
on  the  weight,  length,  and  form  of  the  magnet,  as  well 
as  upon  the  strength  of  its  poles,  and  of  the  "  field  '* 
in  which  it  may  be  placed. 

121.  We  can  use  this  method  to  compare  the  intensity 
01  the  force  of  the  earth's  magnetism2  at  any  place  with 
that  at  any  other  place  on  the  earth's  surface,  by  oscil- 
lating a  magnet  at  one  place  and  then  taking  it  to  the 
other  place  and  oscillating  it  there.      If,  at  the  first,  it 
makes  a  oscillations  in  one  minute,  and  at  the  second,  b 
oscillations  a  minute,  then  the  magnetic  forces  at  the 

1  It  is  possible,  also,  to  measure  electrical  forces  by  a  "  method  of  oscil- 
lations ;"  a  small  charged  ball  at  the  end  of  a  horizontally-suspended  arm 
being  caused  to  oscillate  under  the  attracting  force  of  a  charged  conductot 
near  it,  whose  "  force"  at  that  distance  is  proportional  to  the  square  of  the 
dumber  of  oscillations  in  a  given  time. 

1  Or,  more  strictly,  of  its  Horizontal  co 


100 


ELEMENTARY  LESSONS  ON        [CH..P.  n. 


two  places  will  be  to  one  another  in  the  ratio  of  a2 
to  b\ 

Again,  we  may  use  the  method  to  compare  the  force 
exerted  at  any  point  by  a  magnet  near  it  with  the  force 
of  the  earth's  magnetism  at  that  point.  For,  if  we  swing 
a  small  magnetic  needle  there,  and  find  that  it  makes  m 
oscillations  a  minute  under  the  joint  action 1  of  the  earth's 
magnetism,  and  that  of  the  neighbouring  magnet,  and 
that,  when  the  magnet  is  removed,  it  makes  n  oscillations 
a  minute  under  the  influence  of  the  earth's  magnetism 
alone,  then  mz  will  be  proportional  to  the  joint  forces, 
»2  to  the  force  due  to  the  earth's  magnetism,  and  the 
difference  of  these,  or  ;;z2  —  ;/2  will  be  proportional  to  the 
force  due  to  the  neighbouring  magnet. 

122.  We  will  now  apply  the  method  of  oscillations  to 
measure  the  relative  quantities  of  free  magnetism  at 
different  points  along  a  bar  magnet.  The  magnet  to 
be  examined  is  set  up  vertically  (Fig.  56).  A  small 
magnet,  capable  of  swinging  horizontally,  is  brought  near 
it  and  set  at  a  short  distance  away 
from  its  extremity,  and  then  oscillated, 
while  the  rate  of  its  oscillations  Is 
counted.  Suppose  the  needle  were 
such  that,  when  exposed  to  the  earth's 
magnetism  alone,  it  would  perform  3 
complete  oscillations  a  minute,  and 
that,  when  vibrating  at  its  place  near 
the  end  of  the  vertical  magnet  it 
oscillated  14  times  a  minute,  then 
the  force  due  to  the  magnet  will  be 
proportional  to  J4a  —  32=  196  —  9  = 
187.  Nextly,  let  the  oscillating  mag- 
net be  brought  to  an  equal  distance 
opposite  a  point  a  little  away  from 
the  end  of  the  vertical  magnet.  If,  here,  it  oscillated 

1  We  are  here  assuming  that  the  magnet  is  so  placed  that  its  force  is  in  a 
line  with  that  of  the  earth's  magnetism  at  the  point,  and  that  the  other  pole 
ot  the  ma-met  is  so  far  away  as  not  to  affect  the  oscillating  needle. 


12— 

10  — 

ft™  —  " 

B- 

5   — 

A- 

3 


Fig.  56. 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM. 


101 


12  times  a  minute,  \ve  know  that  the  force  will  be  pro- 
portional to  I22— 32=  144  —  9  =  135.  So  we  shall  find 
that  as  the  force  falls  off  the  oscillations  will  be  fewer, 
until,  when  we  put  the  oscillating  magnet  opposite  the 
middle  of  the  vertical  magnet,  we  shall  find  that  the 
number  of  oscillations,  is  3  per  minute,  or  that  the 
earth's  force  is  the  only  force  affecting  the  oscillations. 
In  Fig.  57  we  have  indicated  the  number  of  oscillations 
at  successive  points,  as  14,  12,  10,  8,  6,  5,  4,  and  3. 
If  we  square  these  numbers  and  subtract  9  from  each, 
we  shall  get  for  the  forces  at  the  various  points  the 
following: — 187,  135,  91,  55,  27,  16,  7,  and  o.  These 
forces  may  be  taken  to  represent  the  strength  of  the 
free  magnetism  at  the  various  points,  and  it  is  convenient 
to  plot  them  out  graphically  in  the  manner  shown  in 


Fie.  57. 


Fig.  57,  where  the  heights  of  the  dotted  lines  are  chosen 
to  a  scale  to  represent  proportionally  the  forces.  The 
curve  which  joins  the  tops  of  these  "  ordinates  "  shows 
graphically  how  the  force,  which  is  greatest  at  the  end, 
falls  off  toward  the  middle.  On  a  distant  magnet  pole 
these  forces,  thus  represented  by  this  curvilinear  triangle, 
would  act  as  if  concentrated  at  a  point  in  the  magnet 


102 


ELEMENTARY  LESSONS  ON        [CHAP.  11. 


opposite  the  "  centre  of  gravity  "  of  this  triangle  ;  or,  in 
other  words,  the  "  pole,"  which  is  the  centre  of  the  result? 
ant  forces,  is  not  at  the  end  of  the  magnet.  In  thin 
bars  of  magnetised  steel  it  is  at  about  -fa  of  the  magnet's 
length  from  the  end. 

123.  Method  of  Deflections. — There  are  a  number 
of  ways  in  which  the  deflection  of  a  magnet  by  another 
magnet  may  be  made  use  of  to  measure  magnetic  forces.1 
We  cannot  here  give  more  than  a  glance  at  first  principles. 
When  two  equal  and  opposite  forces  act  on  the  ends  of 
a  rigid  bar  they  simply  tend  to  turn  it  round.  Such  a 

pair  of  forces  form  what 
is  called  a  "  couple,"  and 
the  effective  power  or 
"  moment "  of  the  couple 
is  obtained  by  multiplying 
one  of  the  two  forces  by 
the  perpendicular  distance 
between  the  directions  of 
the  forces.  Such  a  couple 
tends  to  produce  a  motion 
of  rotation,  but  not  a 
motion  of  translation. 
Now,  a  magnetic  needle 
placed  in  a  magnetic  field 
across  the  lines  of  force, 
experiences  a  "  couple," 
tending  to  rotate  it  round 
Fis-  58.  Jnt0  the  magnetic  meridian, 

for  the  N.  -  seeking  pole  is  urged  northwards,  and 
the  S.-seeking  pole  is  urged  southwards,  with  an  equal 
and  opposite  force.  The  force  acting  on  each  pole 
is  the  product  of  the  strength  of  'the  pole  and  the 
intensity  of  the  "  field,"  that  is  to  say,  of  the  horizontal 
component  of  the  force  of  the  earth's  magnetism  at  the 

1  1  The  student  desirous  of  mastering  these  methods  of  measuring  magnetic 
forces  should  consult  Sir  G.  Airy's  Treatise  on  Magnetism. 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM.  103 

place."  We  will  call  the  strength  of  the  N.-  seeking  pole 
m;  and  we  will  use  the  symbol  H  to  represent  the 
force  exerted  in  a  horizontal  direction  by  the  earth's 
magnetism.  (The  value  of  H  is  different  at  different 
regions  of  the  globe.)  The  force  on  the  pole  A  (see 
Fig-  58)  will  be  then  tn  x  H  or  m  H,  and  that  on  pole 
B  will  be  equal  and  opposite.  We  take  N  S  as  the 
direction  of  the  magnetic  meridian,  and  the  forces  will 
be  parallel  to  this  direction.  Now,  the  needle  A  B  lies 
obliquely  in  the  field,  and  the  magnetic  force  acting  on 
A  is  in  the  direction  of  the  line  P  A,  and  that  on  B  in 
the  direction  Q  B,  a"s  shown  by  the  arrows.  P  Q  is  the 
perpendicular  distance  -between  these  forces  ;  hence  the 
"  moment  "  of  the  couple  will  be  got  by  multiplying  the 
length  P.  Q  by  the.  force  exerted  on  one  of  the  poles. 
Using  the  symbol  G  for  the  moment  of  the  couple  we 
may  write 

G  •=  P  Q  x  ;«-H. 

But  P  Q  is  equal  to  the  length  of  the  magnet  multiplied 
by  the  sine1  of  the  angle  A  O  R,  which  is  the  angle  of 
deflection,  and  which  we  will  call  8.  Hence,  using  /  for 
the  length  between  the  poles  of  the  magnet,  we  may 
write  the  expression  for  the  moment  of  the  couple. 

G  =  m  I H  •  sin  8. 

In  words  this  is  :  the  '•  moment  of  the  couple  "  acting 
on  the  needle  is  proportional  to  its  "  magnetic  moment," 
(m  x  /)  to  the  horizontal  force  of  the  earth's  magnetism, 
and  to  the  sine. of  the  angle  of  deflection. 

The  reader  will  not  have  failed  to  notice  that  if  the 
needle  were  turned  more  obliquely,  the  distance  P  Q 
would  be  longer,  and  would  be  greatest  if  the  needle 
were  turned  round  ensl-and-west,  or  in  the  direction  EW. 
Also  the  "  moment "  of  the  couple  tending  to  rotate  the 
magnet  will  be  less  and  less  as  the  needle  is  turned 
more  nearly  into  the  direction  N  S. 

1  If  any  reader  is  unacquainted  with  trigonometrical  terms  he  should  coo 
suit  the  note  at  the  end  of  this  Lesson,  on  "  Ways  of  reckoning  Angles.'' 


104  ELEMENTARY  LESSONS  ON        [CHAP.  II 

124.  Now,  let  us  suppose  that  the  deflection  $  were 
produced  by  a  magnetic .  force  applied  at  right  angles  to 
the  magnetic  meridian,  and  tending  to  draw  the  pole  A 
in  the  direction  R  A.  The  length  of  the  line  R  T  multi- 
plied by  the  new  force  will  be  the  "  moment "  of  the 
new  couple  tending  to  twist  the  magnet  into  the  .direction 
E  W.  Now,  if  the  needle  has  come  to  rest  in  equilibrium 
between  these  two  forces,  it  is  clear  that  the  two  oppos- 
ing twists  are  just  equal  arid  opposite  in  power,  or  that 
the  moment  of  one  couple  is  equal  to  the  moment  of  the 
other  couple.  Hence,  the  force  in  the  direction  W  E 
will  be  to  the  force  in  the  direction  S  N  in  the  same 
ratio  as  P  Q  is  to  R  T,  or  as  P  O  is  to  R  O. 

Or,  calling  this  force /j 

/ :  H  =  P  O  :  R  O 
Or  /=H- 

But  P  O  =  A  R  and  ±|  =  tan  8  hence 

BO 

/=  H  tan  S; 

or,  in  other  words,  the  magnetic  force  which,  acting  at 
right  angles  to  the  meridian,  produces  on  a  magnetic 
needle  the  defection  8,  is  equal  to  the  horizontal  force  oj 
the  eartWs  magnetism  at  that  point,  multiplied  by  the 
tangent  of  the  angle  of  deflection.  Hence,  also,  two 
different  magnetic  forces  acting  at  right  angles  to  the 
meridian  would  severally  deflect  the  needle  through 
angles  whose  tangents  are  proportional  lo  the  forces. 

This  very  important  theorem  is  applied  in  the  con- 
struction of  certain  galvanometers  (see  Art.  199). 

The  name  Magnetometer  is  given  to  any  magnet 
specially  arranged  as  an  instrument  for  the  purpose 
of  measuring  magnetic  forces  by  the  deflections  they 
produce.  The  methods  of  observing  the  absolute 
values  of  magnetic  forces  in  dynes  or  other  abstract 
units  of  force  will  be  explained  in  the  Note  at  the  end  of 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM.  105 

s 

Lesson  XXV.      See  also  Sir  George  Airv's  Treatise  on 

Magnetism. 

125.  Unit  Strength  of  Pole.— We  found  in  Cou- 
lomb's  torsion-balance  a  convenient  means  of  comparing 
the  strengths  of  poles  of  different  magnets  ;  for  the  force 
which  a  pole  exerts  is  proportional  to  the  strength  of  the 
pole.  The  Second  Law  of  Magnetic  Force  (see  Art. 
1 1 6)  stated  that  the  force  exerted  between  two  poles 
was  proportional  to  the  product  of  their  strengths,  and 
was  inversely  proportional  to  the  square  of  the  distance 
between  them.  It  is  possible  to  choose  such  a  strength 
of  pole  that  this  proportionality  shall  become  numerically 
an  equality.  In  order  that  this  may  be  so,  we  must 
adopt  the  following  as  our  unit  of  strength  of  a  pole,  or 
unit  magnetic  pole  :  A  Unit  Magnetic  Pole  is  one  of  such 
a  strength  that,  when  placed  at  a  distance  of  one  cenli- 
met)e  from  a  similar  pole  of  equal  strength  it  repels  it 
with  a  force  of  one  dyne  (see  Art.  255).  If  we  adopt 
this  definition  we  may  express  the  second  law  of  magnetic 
foice  in  the  following  equation  : — 


where  /  is  the  force  (in  dynes),  ;//  and  in'  the  strengths 
of  the  two  poles,  and  d  the  distance  between  them  (in 
centimeties).  This  subject  is  resumed  in  Lesson  XXV., 
Art.  310,  on  the  Theory  of  Magnetic  Potential. 

126.  Theory  of  Magnetic  Curves. — We  saw  (Art 
1 08)  that  magnetic  figures  are  produced  by  iron-filings 
setting  themselves  in  certain  directions  in  the  field  of 
force  aiound  a  magnet.  We  can  now  apply  the  law  of 
inverse  squares  to  aid  as  in  determining  the  direction 
in  which  a  filing  will  set  itself  at  any  point  in  the  field. 
Let  N  S  (Fig.  59)  be  a  long  thin  magnet,  and  P  any 
point  in  the  field  due  to  its  magnetism.  If  the  N.- 
seeking  pole  of  a  small  magnet  be  put  at  P,  it  will  be 
attracted  by  S  and  repelled  by  N  ;  the  directions  of  these 
two  foices  will  be  along  the  lines  P  S  and  P  N.  The 


io6  -ELEMENTARY  LESSONS_ON       [CHAP.  n. 

jt    •  <a(  ^ 

amounts  of  the  forces  may  be  represented  by  certain 
lengths  marked  out  along  these  lines.  V  ,  Suppose  the 
distance  P  N  is  twice  as  great  as  P  S,  the  repelling  force 
along  P  N  will  be  £  as  strong  as  the  attracting  force 
along  P  S.  So  measure  a  distance  out,  P  A  towards  S 
four  times  as  long  as  the  length  P  B  measured  along  P  N 
away  from  N.  Find  the  resultant  force1  in  the  usual 
way  of  compounding  mechanical  forces,  by  completing 
the  parallelogram  PARE,  and  the  diagonal  P  R  represents 
by  its  length  and  direction  the  magnitude  and  the 


Fig.  59- 

direction  of  the  resultant  magnetic  force  at  the  point  P. 
In  fact  the  line  P  R  represents  the  line  along  which  a 
small  magnet  or  an  iron  riling  would  set  itself.  In  a 
similar  way  we  might  ascertain  the  direction  of  the  lines 
of  force  at  any  point  of  the  field.  The  little  arrows  in 
Fig.  59  show  how  the  lines  of  force  start  out  from  the  N. 
pole  and  curve  round  to  meet  in  the  S.  pole.  The 
student  should  compare  this  figure  with  the  lines  of 
filings  of  Fig.  50. 

1  See  Balfour  Stewart's  Lessons  in  Elementary  Physics,  page  26 ;   or 
Todhunter's  Natural  Philosophy  for  Beginners,  page  55. 


CHAP.  ii.  1    ELECTRICITY  AND  MAGNETISM.  10? 

127.  Force  due  to  a  Magnetic  Shell. — A  mag- 
netic shell  (Art.  107)  exerts  a  magnetic  force  upon  a  mag- 
net pole  placed  at  a  point  in  its  neighbourhood.     If  the 
shell  be  flat  and  very  great,  as  compared  with  the  distance 
of  the  point  considered,  this  force  will  be  independent  of 
that  distance,  will  be  normal  to  the  shell  in  direction,  and 
will  depend  only  upon  the  amount  of  magnetism  on  the 
shell,   and   will  be  numerically  equal  to   2ir  times  the 
quantity  of  magnetism  per  square  centimetre l  (i.e.  to 
2 mr  when  <r  is  the  "surface  density"  of  magnetism  on 
the  face  of  the  shell). 

If  the  shell  is  bounded,  however,  by  a  limiting  area, 
the  force  exerted  by  a  shell  upon  a  point  outside  it  will 
be  ^greater  near  to  the  shell  than  at  a  distance  away. 
In  this  case  it  is  most  convenient  to  measure  not  the 
force  but  the  potential  due  to  the  shell.  The  defini- 
tion of  "  magnetic  potential  "  is  given  in  Art.  310  ;  mean- 
time we  may  content  ourselves  with  stating  that  the 
"potential  due  to  a  magnetic  shell  at  a  point  near  ;/,  is 
equal  to  the  strength  of  the  shell  multiplied  by  the  solid 
angle?  subtended  by  the  shell  at  that  point. 

128.  A   Magnetic    Paradox. — If   the    N.-seeking 
pole  of  a  strong  magnet  be  held  at  some  distance  from 
the  N.-seeking  pole  of  a  weak  magnet,  it  will  repel  it ; 
but  if  it  is  pushed  up  quite  close  it  will  be  found  now  to 
attract   it.     This  paradoxical    experiment   is    explained 
by -the  fact  that  the    magnetism    induced  in  the  weak 
magnet  by  the  powerful  one  will  be  of  the  opposite  kind, 
and  will  be  attracted ;  and,  when  the  powerful  magnet  is 
near,  this  induced  magnetism  may  overpower  and  mask 
the    original    magnetism    of   the    weak    magnet      The 
student  must  be  cautioned  that  in  most  of  the  experi- 
ments on  magnet  poles  similar  perturbing  causes  are  at 
work.     The  magnetism  in  a  magnet  is  not  quite  fixed, 

i  The  proof  of  this  proposition  is  similar  to  that  given  at  end  of  Lesson 
XX.,  for  the  analogous  proposition  concerning  the  for«e  due  to  a  flat  plate 
charged  with  electricity. 

«  Sec  Nots  on  "  Ways  of  Reckoning  Angles,"  at  the  end  of  this  Lesson. 


io8  ELEMENTARY  LESSONS  ON        [CHAP.  n. 

but  is  liable  to  be  disturbed  in  its  distribution  by  the 
near  presence  of  other  magnet  poles,  for  no  steel  is  so 
hard  as  not  to  be  temporarily  affected  by  magnetic 
induction.  The  law  of  inverse  squares  is  only  true  when 
the  distance  between  the  poles  is  so  great  that  the  dis- 
placement of  their  magnetism  due  to  mutual  induction 
is  so  small  that  it  may  be  neglected. 


NOTE  ON  WAYS  OF  RECKONING  ANGLES  AND 
SOLID-ANGLES. 

129.  Reckoning  in  Degrees. — When  l\vo  straight  lines  cross 
one  another  they  form  an  angle  between  them  ;  and  this  angle 
may  be  defined  as  the  amount  of  rotation  which  one  of  the  lines 
has  performed  round  a  fixed  point  in  the  other  line.     Thuj  we 

may  suppose  the  line  C  P  in  Fig.  60  to 
have  originally  lain  along  C  O,  and  then 
turned  round  to  its  present  position.  The 
amount  by  which  it  has  been  rotated  is 
clearly  a  certain  fraction  of  the  whole  way 
round  ;  and  the  amount  of  rotation  round 
C  we  call  "  the  angle  which  P  C  makes 
with  O  C,"  or  more  simply  "  the  angle 
PCO."  But  there  are  a  number  of 
different  ways  of  reckoning  this  angle. 
The  common  v/ay  is  to  reckon  the  angle 
Thus,  suppose  a  circle  to  be  drawn 
round  C,  if  the  circumference  of  the  circle  were  divided  into 
360  parts  each  part  would  be  called  "one  degree "  (l°),  and 
the  angle  would  be  reckoned  by  naming  the  number  of  such 
degrees  along  the  curved  arc  O  P.  In  the  figure  the  arc  is 

about  57 1°,  or  ^  of  the  whole  way  round,  no  matter  what  size 

the  circle  is  drawn. 

130.  Reckoning  in  Radians. — A  more   sensible  but   less 
usual  way  to  express  an  angle  is  to  reckon  it  by  the  ratio  between 
the  length  of  the  curved  arc  that  "subtends"  the  angle  and  the 
length  of  the  radius  of  the  circle.     Suppose  we  have  drawn 
round  the   centre   C   a  circle  whose  radius  is  one  centimetre, 
the    diameter  will   be    two    centimetres.      The    length   of  tho 
circumference   all   round   is   known   to  be   about  3^  times  the 

length  of  the  diameter,    or   more  exactly  3'I4I59 

This  number  is  so  awkward  that,  for  convenience,  we  always 


CHAP,  ii.]   ELECTRICITY  AND  MAGNETISM. 


109 


Hse  for  it  the  Greek  letter  IT.  Hence  the  length  of  the  circum- 
ference of  our  circle,  whose  radius  is  one  centimetre,  will  be 
6 "283 1 8  .  .  .  centimetres,  or  2ir  centimetres.  We  can  then 
reckon  any  angle  by  naming  the  length  of  arc  that  subtends  it 
on  a  circle  one  centimetre  in  radius.  If  we  choose  the  angle 
P  C  O,  such  that  the  curved  arc  O  P  shall  be  just  one  centimetre 
long,  this:  will  be  the  angle  one,  or  unit  of  angular  measure,  or, 
as  it  is  sometimes  called,  the  angle  PCO  will  be  one  "radian." 

^60° 
In  degree-measure  one  radian  =  - —  =  57°  17'  nearly.     All  the 

way  round  the  circle  will  be  2-rr  radians.  A  right-angle  will  be 
^  radians. 

\  -131.  Reckoning  by  Sines  or  Cosines. —  In  trigonometry 
other  ways  of  reckoning  angles  are  used,  in  which,  however,  the 
angles  themselves  are  not  reckoned,  but 
certain  "functions"of  them  called  "sines," 
"cosines,"  " tangents,"  etc.  For  readers 
not  a'ccustomed  to  these  we  will  briefly  ex-  f 
plain  the  geometrical  nature  of  these  ' 
''functions/'  Suppose  we  draw  (Fig.  61)  I 
our  circle  as  before  round  centre  C,  and 
then  drop  down  a  plumb-line  P  M,  on 
to  the  line  CO;  we  will,  instead  of  reckon- 
ing the  angle  by  the  curved  arc,  reckon  it 
by  the  length  of  the  line  P  M.  It  is  clear 
that  if  the  angle  is  small  PM  will  be  short  ;  but  as  the  angle 
opens  out  towards  a  right  angle,  P  M'  will  get  longer  and 
fonger  (Fig.  62).  .The  ratio  between  the  length  of  this  line  and 
the  radius  of  the  circle  is  called  the  "sine" 
of  the  angle,  and  if  the  radius  is  I  the 
length  of  P  M  will  be  the  value  of  the  sine. 
It  can  never  be  greater  than  I,  though  it 
may  have  all  values  between  I  and  -  I. 
The  length  of  the  line  C  M  will  also 
depend  upon  the  amount  of  the  angle.  If 
the  angle  is  small  C  M  will  be  nearly  as 
long  as  CO;  if  the  angle  open  out  to  nearly  a  right  angle 
C  M  will  be  very  short.  The  length  of  C  M  (when  the  radius 
is  I)  is  called  the  "cosine"  of  the  angle.  If  the  angle  be 
called  0,  then  we  may  for  shortness  write  these  functions: 

PM 
Sin  0=  T^p 


Fig.  61. 


= 

132.  Reckoning  by  Tangents.— Suppose  we  draw  our  circle< 


no 


ELEMENTARY  LESSONS  ON         [CHAP.  n. 


as  before  (Fig.  63),  but  at  the  point  O  draw  a  straight  line 
touching  the  circle,  the  tangent  line  at  O  : 
let  us  also  prolong  C  P  until  it  meets  the 
tangent  line  at  T.  We  may  measure  the 
angle  between  O  C  and  O  P  in  terms  of 
the  length  of  the  tangent  O  T  as  compared 
with  the  length  of  the  radius.  Since  our 
radius  is  I,  this  ratio  is  numerically  the 
length  of  O  T,  and  we  may  therefore  call 
the  length  of  O  T  ike  "tangent"  of  t Jit 
angle  O  C  P.  It  is  clear  that  smaller  angles 
will  have  smaller  tangents,  but  that  larger 
angles  may  have  very  large  tangents ;  in 
fact,  the  length  of  the  tangent  when  P  C  was 
moved  round  to  a  right  angle  would  be 
infinitely  great.  It  can  be  shown  that  the 
ratio  between  the  lengths  of  the  sine  and 


C     M 


Fig.  63. 


of  the  cosine  of  the  angle  is  the  same  as  the  ratio  between  the 
length  of  the  tangent  and  that  of  the  radius  ;  or  the  tangent  of 
an  angle  is  equal  to  its  sine  divided  by  its  cosine.  The  formula 
for  the  tangent  may  be  written  : 


133.  Solid  Angles.  —  When  three  or  more  surfaces  intersect 
at  a  point  they  form  a  solid  angle;  there  is  a  solid  angle,  for 
example,  at  the  top  of  a  pyramid,  or  of  a  cone,  and  one  at  every 
corner  of  a  diamond  that  has 
been  cut.  If  a  surface  of  any 
given  shape  be  near  a  point,  it 
is  taid  to  subtend  a  certain  solid 
angle  at  that  point,  the  solid 
angle  being  mapped  out  b,y 
drawing  lines  from  all  points 
cf  the  edge  of  this  surface  to  the 
point  P  (Fig.  64.  )  An  irregular 
cone  will  thus  be  generated 
whose  solid  angle  Is  the  solid 
angle  subtended  at  P  by  the 
surface  E  F.  To  reckon  this 


Fig.  64. 


solid  angle  we  adopt  an  expedient  similar  to  that  adopted  when 
we  wished  to  reckon  a  plane  angle  in  radians.  About  the  point 
P,  with  radius  of  I  centimetre,  describe  a  sphere,  which  will 
intercept  the  cone  over  an  area  M  N  :  the  area  thus  intercepted 
measures  the  solid  angle.  If  the  sphere  have  the  radius  I,  its 
total  surface  is  417-.  The  solid  angle  subtended  at  the  centre  by 
a  hemisphere  would  be  2v. 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM. 


il) 


TABLE  OF  NATURAL  SINES  AND  TANGENTS. 


1 

Arc. 

Sine. 

Tangent. 

0° 

o-ooo 

o.ooo 

90° 

1 

•017 

•017 

89 

2 

•035                               -035 

88 

3 

•052 

•052 

87 

4 

•070 

'070 

86 

5 

•087 

•087 

85 

6 

•105 

•105 

84 

7 

•122 

•123 

83 

8 

•139 

•141 

82 

9 

•I56 

'  1  58 

81' 

10 

•174 

•176 

8b! 

15 

•259 

•268 

751 

20 

•342 

•364 

70 

25 

•423 

•466 

65 

30 

•500 

•577 

60 

35 

•574 

•700 

55 

40 

•643 

•839 

50 

45 

•707 

i  -poo 

45 

5° 

•766 

1-192 

40 

55 

•819 

1-428 

35 

60 

•866 

1-732 

65 

•906 

2-145 

25 

70 

•940 

2-747 

20 

75 

•966 

3-732 

15 

80 

•985 

5-671 

10 

81 

•988 

6-314 

9 

82 

•990 

7-115 

8 

83 

'993 

8-144 

7 

84 

'995 

9-514 

6 

85 

•996 

"'43 

5 

86 

•998 

14-30 

4 

87 

'999 

19-08 

3 

88 

'999 

28-64 

2 

89 

'999 

57-29 

I 

90 

i  -ooo 

Infin. 

0 

Co  sine. 

Co-  tangent. 

Arc. 

112 


ELEMENTARY  LESSONS  ON        [CHAP.  11. 


LESSON  XII. — Terrestrial  Magnetism. 

134.  The  Mariner's  Compass. — It  was  mentioned 
in  Art.  79  that  the  compass  sold  by  opticians  consists  of 
a  magnetised  steel  needle  balanced  on  a  fine  point  above 
a  card  marked  out  N,  S,  E,  W,  etc.  The  Mariner's 
Compass  is,  however,  somewhat  differently  arranged. 

In  Fig.  65  one  of  the  forms  of  a  Mariner's  Compass, 
used  for  nautical  observations,  is  shown.  •  Here  the 


Fig.  65. 

card,  divided  out  into  the  32  "  points  of  the  Compass,"  is 
itself  attached  to  the  needle,  and  swings  round  with  it  so 
that  the  point  marked  N  on  the  card  always  points  to 
the  north.  In  the  newest  and  best  ships'  compasses 
several  magnetised  needles  are  placed  side  by  side,  as  it 
is  found  that  the  indications  of  such  a  compound  needle 
are  more  reliable.  The  iron  fittings  of  wooden  vessels, 
and,  in  the  case  of  iron  vessels,  the  ships  themselves, 


CHAP.  11. J    ELECTRICITY  AND  MAGNETISM.    '         113 

affect  the  compass,  which  has  therefore  to  be  corrected 
by  placing  compensating  masses  of  iron  near  it,  or  by 
fixing  it  high  upon  a  mast. 

135.  The  Earth  a  Magnet. — Gilbert  made  the  great 
discovery  that  the    compass   needle    points   north    and 
south   because  the  earth  is  itself  also  a  great  magnet. 
The** magnetic    poles    of  the   earth    are,    however,    not 
exactly  at  the  geographical  north  and  south  poles.     The 
magnetic    north  pole  of  the  earth  is  more   than   1000 
miles   away   from  the  actual    pole,  being  in  lat.  70°  5' 
N.,  and  long.  96°  46'  W.      In   1831,  it  was  found  by 
Sir  J.   C.   Ross  to  be  situated    in    Boothia    Felix,   just 
within  the  Arctic  Circle.     The  south  magnetic  pole  of 
the  earth   has  never  been  reached  ;  and  by  reason  of 
irregularities  in  the  distribution  of  the  magnetism  there 
appear  to  be  two  south  magnetic  polar  regions. 

136.  Declination. — In  consequence  of  this  natural 
distribution   the  compass-needle  does   not  at  all  points 
of    the    earth's    surface    point    truly    north    and    south. 
Thus,  in  1881,  the  compass-needle  at  London  points  at 
an  angle  of  about  i8°33'  west  of  the  true  north.     This 
angle  between  the  "magnetic  meridian"1  and  the  geo- 
graphical  meridian   of  a   place  is   called  the   magnetic 
Declination    of   that   place       The  existence   of    this 
declination  was  discovered  by  Columbus  in  1492,  though 
it  appears  to  have  been  previously  known  to  the  Chinese, 
and  is  said  to  have  been  noticed  in  Europe  in  the  early 
part   of  the    I3th  century  by  Peter   Pellegrinus.      The 
discovery  is  also  claimed,  though  on  doubtful  authority, 
for    Sebastian    Cabot    of   Bristol.      The   fact    that    the 
declination  differs  at  different  points  of  the  earth's  sur- 
face, is  the  undisputed  discovery  of  Columbus. 

In  order  that  ships  may  steer  by  the  compass,  mag- 
i 

1  The  Magnetic  Meridian  of  any  place  is  an  imaginary  plane  drav/n 
through  die  zenith,  and  passing  through  the  magnetic  north  point  and  mag- 
netic south  point  of  the  horizon,  as  observed  at  that  place  by  the  pointing  of 
a  horizontally-suspended  compass-needle. 

1 


ELEMENTARY  LESSONS  ON        [CHAP.  n. 


netic  charts  (Art.  139)  must  be  prepared,  and  the  declina- 
tion at  different  places  accurately  measured.  The  upright 
pieces  P  P',  on  the  "  azimuth  compass  "  drawn  in  Fig. 
65,  are  for  the  purpose  of  sighting  a  star  whose  position 
may  be  known  from  astronomical  tables,  and  thus 
affording  a  comparison  between  the  magnetic  meridian 
of  the  place  and  the  geographical  meridian,  and  of 
measuring  the  angle  between  them. 

137.  Inclination  or  Dip. — Norman,  an  instrument- 
maker,  discovered  in.  1576  that  a  balanced  needle, 
when  magnetised,  tends  to  dip  downwards  toward  the 

north.  He  there- 
fore constructed  a 
Dipping  -Needle, 
capable  of  turning 
in  a  vertical  plane 
about  a  horizontal 
axis,  with  which  he 
found  the  "dip" 
to  be  (at  London) 
an  angle  of  71°  50'. 
A  simple  form  of 
Dipping-needle  is 
shown  in  Fig.  66. 
The  dip  -  circles 
used  in  the  mag- 
netic observatory 
at  Kew  are  much 
more  exact  and 
delicate  instru- 

- 66-  ments.        It    was, 

however,  found  that  the  dip,  like  the  declination,  differs 
at  different  parts  of  the  earth's  surface,  and  that  it 
also  undergoes  changes  from  year  to  year.  The  "dip" 
in  London  for  the  year  1881  is  67°  39'.  At  the 
north  magnetic  pole  the  needle  dips  straight  down. 
The  following  table  gives  particulars  oJ  the  Declination^ 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM. 


Inclination,  and  total  magnetic  force  at  a  number  of 
important  places,  the  values  being  approximately  true 
for  the  year  1880. 

TABLE  OF  MAGNETIC  DECLINATION  AND  INCLINATION 
(for  Year  1880.) 


Declination. 

Inclination. 

Total  force  (in 
C.  G.  S.unitb). 

Boothia  Felix 

(None.) 

90°        N 

•6S 

London 

lS°  40'  W 

67°  40'  N 

'47 

St.  Petersburg 

0°  40'  W 

70°        N 

•48 

Berlin  . 

n°  30'  W 

64°        N 

•48 

Paris    . 

16°  45'  W 

66°        N 

•47 

Rome  . 

11°  30'  W 

60°        N 

•45 

New  York     . 

7°  57'  W 

72°  i2'N 

•6  1 

Mexico 

7°  55'  E 

*5°  ?    N 

•48 

Quito   . 

7°  40'  E 

25°  ?    N 

•35 

St.  Helena    . 

26  J  25'  W 

28°        S 

•31 

Cape  Town  . 

30°  2r  W 

56°  30'  s 

•36 

Sydney 

9°  30'  E 

62°  45'  S 

'57 

Hobarlon 

8°  49'  E 

7i°  5'    S 

•04 

Tokio  . 

4°  5'    W 

50°        N 

'45 

138.  Intensity.  —  Three  things  must  be  known  in 
order  to  specify  exactly  the  magnetism  at  any  place ; 
these  three  elements  are  : 

The  Declination  ; 

The  Inclination,  and 

The  Intensity  of  the  Magnetic  Force. 

The  magnetic  force  is  measured  by  one  of  the 
methods  mentioned  in  the  preceding  Lesson.  Its 
direction  is  in  the  line  of  the  dipping-needle,  which,  like 
every  magnet,  lends  to  set  itself  along  the  lines-of-force. 
It  is,  however,  more  convenient  to  measure  the  force 
not  in  its  total  intensity  in  the  line  of  the  dip,  but  to 
measure  the  horizontal  component  of  the  force,  —  that 
is  to  say,  the  force  in  the  direction  of  the  homontal 
compass -needle,  from  which  the  total  force  can  be 


n6  ELEMENTARY   LESSONS  ON         [CHAP.  it. 

calculated  if  the  dip  is  known.  Or  if  the  horizontal 
and  vertical  components  of  the  force  are  known,  the 
total  force  and  the  angle  of  the  dip  can  both  be  cal- 
culated.1 The  horizontal  component  of  the  force,  or 
"  horizontal  intensity,"  can  be  ascertained  either  by  the 
method  of  Vibrations  or  by  the  method  of  Deflexions. 
The  mean  horizontal  force  of  the  earth's  magnetism  at 
London  in  1880  was  'i8  dyne-units,  the  total  force  (in 
the  line  of  dip)  is  "47  dyne-units.  The  distribution  of 
the  magnetic  force  at  different  points  of  the  earth's 
surface  is  irregular,  and  varies  in  different  latitudes 
according  to  an  approximate  law,  which,  as  given  by 
Biot,  is  that  the  force  is  proportional  to  Vi  +  3  sin5/. 
where  /  is  the  magnetic  latitude. 

139.  Magnetic  Maps. — For  purposes  of  conveni- 
ence it  is  usual  to  construct  magnetic  maps,  on  which 
such  data  as  these  given  in  the  Table  on  p.  115  can  be 
marked  down.  Such  maps  may  be  constructed  in 
several  ways.  Thus,  it  would  be  possible  to  take  a  map 
of  England,  or  of  the  world,  and  mark  it  over  with  lines 
such  as  to  represent  by  their  direction  the  actual 
direction  in  which  the  compass  points ;  in  fact  to  draw 
the  lines  of  force.  A  more  useful  way  of  marking  the 
map  is  to  find  out  those  places  at  which  the  declination 
is  the  same,  and  to  join  these  places  by  a  line.  The 
Magnetic  Map  of  England  which  forms  the  Frontis- 
piece to  these  Lessons  is  constructed  on  this  plan.  At 
Bristol  the  compass-needle  in  1888  will  point  19°  to 
the  west  of  the  geographical  north.  The  declination  at 
Torquay,  at  Stafford,  at  Leeds,  and  at  Hartlepool,  will  in 
that  year  be  the  same  as  at  Bristol.  Hence  a  line  joining 
these  towns  may  be  called  a  line  of  equal  declination^  or 
an  Isogonic  line.  It  will  be  seen  from  this  map  that  the 
declination  is  greater  in  the  north-west  of  England  than 

i  For  if  H  =  Horizontal  Component  of  F^rce    and  I  =  Total  Force,  and  { 
=-  angle  of  dip,  I  =  H  -:  co.  Q. 
»  For  H»  +  V>=  13,  where  V  =.  Vertical  Component  of  Force. 


CHAP,  ii.]    ELECTRICITY  AND  MAGNETISM. 


117 


in  the  south-east.  We  might  similarly  construct  a 
magnetic  map,  marking  it  with  lines  joining  places 
where  the  dip  was  equal ;  such  lines  would  be  called 
Isoclinic  lines.  In  England  they  run  across  the  map 
f  om  west-south-west  to  east-north-east.  On  the  globe 


Fig.  67. 

the  isogonic  lines  run  for  the  most  part  from  the  nofth 
magnetic  pole  to  the  (south  magnetic  polar  region,  but, 
owing  to  the  irregularities  of  distribution  of  the  earth's 
magnetism,  their  forms  are  not  simple.  The  isoclinic 
lines  of  the  globe  run  round  the  earth  like  the  parallels 


1 18  ELEMENTARY  LESSONS  ON        [CHAP.  ir. 

of  latitude,  but  are  irregular  in  form.  Thus  the  line 
joining  places  where  the  north-seeking  pole  of  the 
needle  dips  down  70°  runs  across  England  and  Wales, 
passes  the  south  of  Ireland,  then  crosses  the  Atlantic  in 
a  south-westerly  direction,  traverses  the  United  States, 
swerving  northwards,  and  just  crosses  the  southern  tip 
of  Alaska.  It  drops  somewhat  southward  again  as  it 
crosses  China,  but  again  curves  northwards  as  it  enters 
Russian  territory.  Finally  it  crosses  the  southern  part 
of  the  Baltic,  and  reaches  England  across  the  German 
Ocean.  The  chart  of  the  world,  given  in  Fig.  67,  shows 
the  isoclinic  lines  of  the  Northern  Hemisphere,  and  also 
a  system  of  "  terrestrial  magnetic  meridians "  meeting 
one  another  in  the  North  Magnetic  pole  at  A.  It  was 
prepared  by  the  Astronomer-Royal,  Sir  George  Airy,  for 
his  Treatise  on  Magnetism. 

140.  Variations    of    Earth's    Magnetism. — We 
have  already  mentioned  that  both  the  declination  and 
the   inclination  are   subject   to  changes ;  some   of  these 
changes  take  place  very  slowly,  others  occur  every  year, 
and  others  again  eVery  day. 

141.  Secular  Changes. — Those  changes  which  re- 
quire many  years  to  run  their  course  are  called  secular 
changes. 

The  variations  of  the  declination  previous  to  1580 
are  not  recorded  ;  the  compass  at  London  then  pointed  1 1° 
east  of  true  north.  This  easterly  declination  gradually  de- 
creased, until  in  1657  the  compass  pointed  true  north. 
It  then  moved  westv/ard,  attaining  a  maximum  of  24° 
27'  about  the  year  1816,  from  which  time  it  has  slowly 
diminished  to  its  present  value  of  18°  33' ;  it  diminishes 
(in  England)  at  about  the  rate  of  7'  per  year.  At 
about  the  year  1976  it  will  again  point  truly  north, 
making  a  complete  cycle  of  changes  in  about  320  years. 

The  Inclination  in  1576  was  71°  50',  and  it  slowly 
increased  till  1720,  when  the  angle  of  dip  reached 
the  maximum  value  of  74°  42'.  It  has  since  steadily 


CHAP,  ii.]    ELECTRICITY.  AND  MAGNETISM. 


119 


diminished  to  its  present  value  of  67°  39'.  The  period  in 
which  the  cycle  is  completed  is  not  known,  but  the  rate 
of  variation  of  the  dip  is  less  at  the  present  time  than  it 
was  fifty  years  ago.  In  all  parts  of  the  earth  both  declin- 
ation and  inclination  are  changing  similarly.  The  follow- 
ing table  gives  the  data  of  the  secular  changes  at  London. 

TABLE  OF  SECULAR  MAGNETIC  VARIATIONS. 


Ye'ar. 

Declination. 

Inclination. 

1576 

7»°  50' 

1580 

11°  17'  E. 

1600 

72°  o' 

1622 

6°  12 

1634 

4°o' 

1657 

0°  0'  min. 

1676 

3°  o'  W. 

73°  30' 

1705 

9°o' 

r72o 

•  3"°' 

74°  42  ma*. 

1760 

jo°  30 

1780 

72°  8' 

.1800 

2.T  r/ 

70°  35' 

1816 

24°  30'  max. 

1830 

24'  2' 

69"  3' 

i855 

23°  o' 

1868 

20°  33' 

68*2' 

1878 

19°   14 

<>r  43 

1880 

18'  40' 

67°  40 

1888 

17°  40' 

67°  25'  (,') 

The  Total  Magnetic  forcf,  or  "  Intensity,"  also 
slowly  changes  in  value.  As  measured  near  London  it 
was  equal  to  '4791  dyne-units  in  1848,  '4740  in  1866, 
and  at  the  beginning  of  1880,  -4736  dyne-units.1  Owing 
to  the  steady  decrease  of  the  angle  at  which  the  needle 
dips,  the  horizontal  component  of  this  force  (i.e.  the 
"  Horizontal  Intensity  ")  is  slightly  increasing,  ft  was 
•1716  dyne-units  in  1848,  and  '1797  dyne-units  at  the 
beginning  of  1880. 

1  Thai  is  to  say.  a  north  magnet  pole  of  unit  strength  is  urged  in  I  lie  1m* 
of  Jip,  with  a  mechanical  force  of  a  liilli-  Ics*  than  Haifa  JyiT* 


120  ELEMENTARY  LESSONS  ON        [niAp.  11. 

142.  Daily  Variations. — Both  com  pass  and  dipping 
needle,  if  minutely  observed,  exhibit  slight  daily  motions. 
About  7  a.m.  the  compass  needle  begins  to  travel  west 
ward  with  a  motion  which  lasts  till  about  I  p.m.  ;  during 
the  afternoon  and  evening  the  needle  slowly  travels  back 
eastward,  until  about   10  p.m.  :  after  this  it  rests  quiet; 
but  in  summer-time  the  needle  begins  to  move  again 
slightly  to  the  west  at  about  midnight,  and  returns  again 
eastward  before  7  a.n..     These  delicate  variations—  never 
more  than  10'  of  arc — appear  to  be  connected  with  the 
position  of  the  sun ;    and  the    moon    also   exercises   a 
minute  influence  upon  the  position  of  the  needle. 

143.  Annual  Variations. — There  is  also  an  annual 
variation  corresponding  with  the  movement  of  the  earth 
around  the  sun.      In  the  British   Islands  the  total  force 
is  greatest   in  June   and   least   in   February,  but  in  the 
Southern  Hemisphere,  in   Tasmania,  the  reverse  is  the 
case.     The  dip  also  differs  with  the  season  of  the  year, 
the  angle  of  dip  being  (in  England)  less  during  the  four 
summer  months  than  in  the  rest  of  the  year. 

144.  Eleven -Year   Period. — General  Sabine    dis 
covered  that  there  is  a  larger  amount  of  variation  of  the 
declination   occurring   about   once    every  eleven    years. 
Schwabe   noticed  that'  the   recurrence  of  these   periods 
coincided  with  the  eleven-year  periods  at  which  there 
is  a  maximum  of  spots  on  the  sun.      Professor   Balfour 
Stewart  and  others  have  endeavoured  to  trace  a  similar 
periodicity  in  the  recurrence  of  auroras1  and  of  other 
phenomena. 

145.  Magnetic  Storms. — It  is  sometimes  observed 
that  a  sudden  (though  very  minute)  irregular  disturbance 
will  affect  the  whole  of  the  compass  needles  over  a  con- 
siderable region  of  the  globe.     Such   occurrences  are 
known  as   magnetic  storms  ;    they  frequently  occur  at 
the  time  when  an  aurora  is  visible. 

146.  Self-recording  Magnetic  Apparatus. — At 

I  See  Lesson  XXIV.,  on  Atmospheric  Electricity. 


CHAP.  n.J    ELECTRICITY  AND   MAGNETISM.  121 

Kew  and  other  magnetic  observatories  the  daily  and 
hourly  variations  of  the  magnet  are  recorded  on  a 
continuous  register.  The  means  employed  consists  in 
throwing  a  beam  of  light  from  a  lamp  on  to  a  light  mirror 
attached  to  the  magnet  whose  motion  is  to  be  observed. 
A  spot  of  light  is  thus  reflected  upon  a  ribbon  of  photo- 
graphic paper  prepared  so  as  to  be  sensitive  to  light. 
The  paper  is  moved  continuously  forward  by  a  clock- 
work train  ;  and  if  the  magnet  be  at  rest  the  dark  trace 
on  the  paper  will  be  simply  a  straight  line.  If,  however, 
the  magnet  moves  aside,  the  spot  of  light  reflected  from 
the  mirror  will  be  displaced,  and  the  photographed  Hne 
will  be  curved  or  crooked.  Comparison  of  such  records, 
or  "  magnttographs*  from  stations  widely  apart  on  the 
earth's  surface,  promises  to  afford  much  light  upon  the 
cause  of  the  earth's  magnetism  and  of  its  changes,  of 
which  hitherto  no  reliable  origin  has  been  with  certainty 
assigned. 

The  phenomenon  of  earth  •  currents  (Art.  403)  appears  to  he  connected 
with  that  of  the  changes  in  the  earth's  magnetism,  and  can  be  observed 
whenever  there  is  a  display  of  aurora,  and  during  a  magnetic  storm  ;  but  it 
is  not  yet  determined  whether  these  currents  are  due  to  the  variations  in  the 
magnetism  of  the  earth,  or  whether  these  variations  are  due  to  the  currents. 
It  is  known  that  the  evaporation  (see  Art.  63)  always  going  on  in  the  tropics 
causes  the  ascending  currents  of  heated  air  to  be  electrified  positively 
relatively  to  the  eai  th.  These  air  currrents  travel  northward  and  southward 
toward  the  colder  polar  regions  where  they  descend.  These  streams  of 
electrified  air  will  act  (see  An.  337)  like  true  electric  currents,  and  as  the 
earth  rotates  within  them  it  will  be  acted  upon  magnetically.  Whether  this 
will  account  for  the  gradual  growth  of  the  earth's  magnetism  is  an  open 
question.  The  action  of  the  sun  and  moon  in  raising  tides  in  the  atmosphere 
might  also  account  for  the  variations  mentioned  in  Art.  142.  It  is  im- 
portant to  note  that  in  all  magnetic  storms  the  intensity  of  the  perturbations 
is  greatest  in  the  regions  nearest  the  poles  ;  also,  that  the  magnetic  poles 
coincide  very  nearly  with  the  regions  c«"  greatest  cold  ;  that  the  region  where 
aurora  (Art.  309)  are  seen  in  greatest  abundance  is  a  region  lying  nearly 
symmetrically  round  the  magnetic  p->le.  It  may  be  added  that  the  general 
direction  of  the  feeble  ilaily  earth  -  currnnts  (Art.  403)  is  from  the  pole» 
toward  r.lie  equator 


122  ELEMENTARY  LESSONS  ON       [CHAP.  ML 


CHAPTER  III. 

CURRENT  ELECTRICITY. 
LESSON  XJII. — Simple  Voltaic  Cells. 

147.  It  has  been  already  mentioned,  in  Lesson  IV, 
now  electricity  flows  away  from  a  charged  body  through 
any  conducting  substance,  such  as  a  wire  or  a  wetted 
string.  If,  by  any  arrangement,  electncity  could  be 
supplied  to  the  body  just  as  fast  as  it  flowed  away,  a 
continuous  current  would  be  produced.  Such  a  current 
always  flows  through  a  conducting  wire,  if  the  ends  are 
kept  at  different  electric  potentials.  In  like  manner, 
a  current  of  heat  flows  through  a  rod  of  metal  if  the 
ends  are  kept  at  different  temperatures,  the  flow  being 
always  from  the  high  temperature  to  the  lower.  It  is 
convenient  to  regard  electricity  as  flowing  from  positive 
to  negative  ;  or,  in  other  words,  the  direction  of  an  electric 
current  is  from  the  high  potential  to  the  low.  It  is 
obvious  that  such  a  flow  lends  to  bring  both  to  one 
level  of  potential.  The  "  current  "  has  sometimes  been 
regarded  as  a  double  transfer  of  positive  electricity  in 
one  direction,  and  of  negative  electricity  in  the  opposite 
direction.  The  only  evidence  to  support  this  very  un- 
necessary supposition  is  the  fact  that,  in  the  decom- 
position of  liquids  by  the  current,  some  of  the  elements 
are  liberated  at  the  point  where  the  potential  is  highest, 
others  at  the  point  where  it  is  lowest. 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  123 

Continuous  currents  of  electricity,  such  as  we  have 
described,  are  usually  produced  by  voltaic  cellst  or 
batteries  of  such  cells,  though  there  are  other  sources  of 
currents  hereafter  to  be  mentioned. 

148.  Discoveries  of  G-alvani  and  of  Volta. — 
The  discovery  of  electric  currents  originated  with  Galvani, 
a  physician  of  Bologna,  who,  about  the  year  1786,  made 
a  series  of  curious  and  important  observations  upon  the 
convulsive  motions  produced  by  the  "  return-shock  "  (Art. 
26)  and  other  electric  discharges  upon  a  frog's  leg.     Ho 
was  led  by  this  to  the  discovery  that  it  was  not  necessary 
to  use  an  electric  machine  to  produce  these  effects,  but 
that  a  similar  convulsive  kick  was  produced  in  the  frog's 
leg  when   two   dissimilar   metals,   iron   and   copper,  for 
example,  were  placed   in   contact  with   a  nerve  and  a 
muscle  respectively,  and  then  brought  into  contact  with 
each  other.     Galvani  imagined  this  action  to  be  due  to 
electricity  generated   by  the  frog's   leg  itself.      It  was, 
however,  proved  by  Volta,  Professor  in  the  University 
of  Pavia,  that  the  electricity  arose  not  from  the  muscle 
or  nerve,  but  from  the  contact  of  the  dissimilar  metals. 
When  two  metals  both  in  contact  with  the  air  or  other 
oxidising  medium  are  placed  in  contact  with  one  another, 
the  surface  of  one  become?  positive  and  of  the  other  nega- 
tive, as  stated  on  p.  67.      Though  the  charges  are  very 
feeble,  Volta  proved  their  reality  by  two  different  methods. 

149.  Contact  Electricity :  Proof  by  the  Con- 
densing Electroscope. — The   first   method   of  proof 
devised  by  Volta  involved  the   use   of  the  Condensing 
Electroscope,  alluded  to  in  Art.  71.      It  can  be  used  in 
the   following  way  to  show  the  production   of  electrifi- 
cation.    A  small  bar  made  of  two  dissimilar  metals,  zinc 
and  copper  soldered  together,  is  held  in  the  hand,  and 
one  end  is  touched  against  the  lower  plate,  the  upper 
plate   being   at   the   same   time    joined   to    "  eartn "   or 
touched   with   the   hand    (Fig.   68).       During   the   con- 
tact electrical  separation  has   taken  place  at  the  point 


I24 


ELEMENTARY  LESSONS  ON       [CHAP.  ill. 


where  the  dissimilar  metals  touched  one  another,  and 

upon  the  plates  of 
the  condenser  the  op- 
posite charges  have 
accumulated.  When 
the  upper  plate  is 
lifted  off  the  lower 
one,  the  capacity  of 
the  condenser  dimin- 
ishes enormously,  and 
the  small  quantity  of 
electricity  is  now  able 
to  raise  the  potential 
of  the  plates  to  a 
higher  degree,  and 
the  gold  leaves  ac- 
cordingly expand.1 

15O.  The  Voltaic 
Pile. — The  second  of 
Volta's  proofs  was  less 
direct,  but  even  more  convincing ;  and  consisted  in 
showing  that  when  a  number  of  such  contacts  of  dis- 
similar metals  could  be  arranged  so  as  to  add  their 
electrical  effects  together,  those  effects  were  more  power- 
ful in  proportion  to  the  number  of  the  contacts.  With 
this  view  he  constructed  the  apparatus  known  (in  honour 
of  the  discoverer)  as  the  Voltaic  Pile  (Fig.  69).  It 
is  made  by  placing  a  pair  of  discs  of  zinc  and  copper 
in  contact  with  one  another,  then  laying  on  the  copper 
disc  a  piece  of  flannel  or  blotting-paper  moistened  with 
brine,  then  another  pair  of  discs  of  zinc  and  copper,  and 
so  on,  each  pair  of  discs  in  the  pile  being  separated 

1  Formerly,  this  action  was  accounted  for  by  saying  that  the  electricity 
which  was  "  bound  "  \vhen  the  plates  of  the  condenser  were  close  together, 
becomes  "  free "  when  the  top  plate  is  lifted  up  ;  the  above  is.  however,  a 
more  scientific  and  more  accurate  way  of  saying  the  same  thing.  The 
student  who  is  unable  to  reconcile  these  two  ways  of  stating  the  matter 
snould  read  again  Articles  47,  48,  on  pp.  53  to  55. 


Fig   68. 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM. 


V>y  a  moist  conductor.  Such  a  pile>  if  composed  of 
a  number  of  such  pairs  of  discs,  will  produce  electricity 
enough  to  give  quite  a  perceptible  shock,  if  the  top  and 
bottom  discs,  or  wires  connected  with 
them,  be  touched  simultaneously  with 
the  moist  fingers.  When  a  single  pair 
of  metals  are  placed  in  contact,  one 
becomes  +  ly  electrical  to  a  certain  small 
extent,  and  the  other  —  ly  electrical,  or  in 
other  words  there  is  a  certain  difference 
of  electric  potential  (see  p.  40)  between 
them.  But  when  a  number  are  thus  set 
in  series  with  moist  conductors  between 
the  successive  pairs,  the  difference  of 
potential  between  the  first  zinc  and  the 
last  copper  disc  is  increased  in  propor- 
tion to  the  number  of  pairs  ;  for  now 


Fig.  69. 


all  the  successive  small  differences  of  potential  are  added 
together. 

151.  The  Crown  of  Cups. — Another  combination 
devised  by  Volta  was  his  Couronne  de  Tosses  or  Crown 
of  Cups.  It  consisted  of  a  number  of  cups  (Fig.  70), 


Fig.  70. 

filled  either  with  brine  or  dilute  acid,  into  which  dipped 
a  number  of  compound  strips,  half  zinc  half  copper, 
the  zinc  portion  of  one  strip  dipping  into  one  cup,  while 


126 


ELEMENTARY  LESSONS  ON      [CHAP.  in. 


the  copper  portion  dipped  into  the  other  cup.  The 
difference  of  potential  between  the  first  and  last  cups 
is  again  proportional  to  the  number  of  pairs  of  metal 
strips.  This  arrangement,  though  badly  adapted  for 
such  a  purpose,  is  powerful  enough  to  ring  an  electric 
bell,  the  wires  of  which  are  joined  to  the  first  zinc  and 
the  last  copper  strip.  The  electrical  action  of  these 
combinations  is,  however,  best  understood  by  studying 
the  phenomena  of  one  single  cup  or  cell. 

152.  Simple  Voltaic  Cell: — Place  in  a  glass  jar  some 
water  having  a  little  sulphuric  acid  or  any  other  oxidising 
acid  added  to  it  (Fig.  71).  Place  in  it  separately  two 

clean  strips,  one  of 
zinc  Z,  and  one  of 
copper  C.  This  cell 
is  capable  of  sup- 
plying a  continuous 
flow  of  electricity 
through  a  wire 
whose  ends  are 
brought  into  con- 
nection with  the 
two  strips.  When 
the  current  flows 
the  zinc  strip  is 
observed  to  waste 
away ;  its  consump- 
tion in  fact  furnishes 
the  energy  required 

Fig.  7i.  to  drive  the  current 

through     the     cell 

and  the  connecting  wire.  The  cell  may  therefore  be 
regarded  as  a  sort  of  chemical  furnace  in  which  the  fuel 
is  zinc.  Before  the  strips  are  connected  by  a  wire  no 
appreciable  difference  of  potential  between  the  copper 
and  the  zinc  will  be  observed  by  an  electrometer; 
because  the  electrometer  only  measures  the  potential  at 


CHAP,  in.)    ELECTRICITY  AND  MAGNETISM.          12? 

a  point  in  the  air  or  oxidising  medium  outside  the  zinc 
or  the  copper,  not  the  potentials  of  the  metals  them- 
stives.  The  zinc  itself  is  at  about  1-86  volts  lower 
potential  than  the  surrounding  oxidising  media  (see  Art. 
422  bis}  ;  while  the  copper  is  at  only  about  -81  volts 
lover,  having  a  less  tendency  to  become  oxidised. 
There  is  then  a  latent  difference  of  potential  of  about 
1-05  volts  between  the  copper  and  the  zinc:  but  this 
produces  no  current  as  long  as  there  is  no  metallic  con- 
tact. If  the  strips  are  made  to  touch,  or  are  joined  by 
a  pair  of  metal  wires,  immediately  there  is  a  rush  oi 
electricity  through  the  metal  from  the  copper  to  the  zinc, 
and  a  small  portion  of  the  zinc  is  at  the  same  time  dis- 
solved away  ;  the  zinc  parting  with  its  latent  energy  as 
its  atoms  combine  with  the  acid.  This  energy  is  ex- 
pended in  forcing  a  discharge  of.  electricity  through  the 
acid  to  the  copper  strip,  and  thence  through  the  wire 
circuit  back  to  the  zinc  strip.  The  copper  strip,  whence 
the  current  starts  on  its  journey  through  the  external 
circuit,  is  called  the  positive  pole,  and  the  zinc  strip  is 
called  the  negative  pole.  If  two  copper  wires  are  united 
to  the  tops  of  the  two  strips,  though  no  current  flows  so 
long  as  the  wires  are  kept  separate,  the  wire  attached  to 
the  zinc  will  be  found  to  be  negative,  and  that  attached 
to  the  copper  positive,  there  being  still  a  tendency  for 
the  »nc  to  oxidise  and  drive  electricity  through  the  cell 
from  zinc  to  copper.  This  state -of  things  is  represented 
in  Fig,,  71  ;  and  this  distribution  of  potentials  led  some 
to  consider  the  junction  of  the  zinc  with  the  copper  wire 
as  the  starting  point  of  the  current.  But  the  real  starting 
point  is  in  the  cell  at  the  surface  of  the  zinc  where 
the  chemical  action  is  furnishing  energy  ;  for  from  this 
point  there  are  propagated  through  the  liquid  certain 
electro-chemical  actions  (more  fully  explained  in  chap, 
xi.)  which  have  the  result  of  constantly  renewing  the 
difference  of  potential  and  supplying  electricity  to  the 
•f  pole  just  as  fast  as  that  electricity  leaks  away  through 


128  ELEMENTARY  LESSONS  ON       [CHAP.  HI 

the  wire  to  the  -  pole.  At  the  same  time  it  will  be 
noticed  that  a  few  bubbles  of  hydrogen  gas  appear  on  iht 
surface  of  the  copper  plate.  Both  these  actions  go  on  ;s 
ong  as  the  wires  are  joined  to  form  a  complete  circuit 

153.  Effects   produced    by  Current.  —  The   car- 
rent    itself   cannot    be    seen   to    flow   through    the    wire 
circuit ;     hence    to    prove    that    any    particular    cell   or 
combination   produces   a    current  requires   a   knowledge 
of  some  of  the  effects  which  currents  can  produce.      These 
are  of  various  kinds.      A  current  flowing  through  a  thin 
wire  will  heat  it  ;  flowing  near  a  magnetic  needle  it  will 
cause    it    to    turn ;    flowing    through    water    and    other 
liquids  it  decomposes  them  ;  and,  lastly,  flowing  through 
the  living  body  or  any  sensitive  portion  of  it,  it  produces 
certain   sensations.      These   effects,   thermal,    magnetic, 
chemical,  and  physiological,  will  be  considered  in  special 
Lessons. 

154.  Voltaic  Battery. — If  a  number  of  such  simple 
cells  are  united  in  series,  the  zinc  plate  of  one  joined  to 
the  copper  plate  of  the  next,  and  so  on,  a  greater  differ- 
ence of  potentials  will  be  produced  between  the  copper 
"  pole  "  at  one  end  of  the  series  and  the  zinc  "  pole  "  at 
the  other  end.      Hence,  when  the  two  poles  are  joined 
by  a  wire  there  will  be  a  more  powerful  flow  of  electricity 
than    one   cell    would   cause.      Such    a    combination   of 
Voltaic  Cells  is  called  a  Voltaic  Battery.1 

155.  Electromotive- Force.  —  The   term   "  eleclro- 
motive-force"  is  employed  to  denote  that  which   moves 
or  tends  to  move  electricity  from  one  place  to  another.2 

'  By  some  writers  the  name  Galvanic  Battery  i«  given  in  honour  of 
Galvanl ;  but  the  honour  is  certainly  Volta's.  The  electricity  that  flows 
thus  in  currents  is  sometimes  called  Voltaic  Electricity,  or  Galvanic 
Electricity,  or  sometimes  even  Galvanism  (!),  but,  as  we  shall  see,  it  differs 
only  in  degree  from  Frictional  or  any  other  Electricity,  and  both  can  flow 
through  wires,  and  magnetise  iron,  and  decompose  chemical  compounds 

5  The  beginner  must  not  confuse  "  Electromotive- force,"  or  that  which 
tends  to  move  electricity,  with  Electric  "/orcftn  or  that  force  with 
which  electricity  tends  to  move  matter.  Newton  has  virtuaJly  defined 
"  force,"  once  for  all,  as  that  which  moves  or  tend*  to  move  matter  \Vhee 


CHAP.  iii.J   ELECTRICITY  AND  MAGNETISM.  129 

For  brevity  we  sometimes  write  it  E.M.F.  In  this 
particular  case  it  is  obviously  the  result  of  the  difference 
of  potential,  and  proportional  to  it.  Just  as  in  water- 
pipes  a  difference  of  level  produces  a  pressure^  and  the 
pressure  produces  zflow  so  soon  as  the  tap  is  turned 
on,  so  difference  oj potential  produces  electromotive-force \ 
and  electromotive-force  sets  up  a  current  so  soon  as  a 
circuit  is  completed  for/the  electricity  to  flow  through. 
Electromotive-force,  therefore,  may  often  be  conveniently 
Expressed  as  a  difference  of  potential,  and  vice  versd; 
but  the  student  must  not  forget  the  distinction. 

156.  Volta's  Laws.— Volta  showed  (Art.  70  that 
the  difference  of  potential  between  two  metals  in  contact 
depended    merely   on  what    metals   they  were,  not   on 
their  size,  nor  on  the  amount  of  surface  in  contact.     He 
also  showed  that  when  a  number  of  metals  touch  one 
another  the  difference  of  potential  between  the  first  and 
last  of  the  row  is   the    same   as    if  they  touched    one 
another  directly.      A  quantitative  illustration  from    the 
researches  of  Ayrton  and  Perry  was  given  in  Art.  72. 
But  the  case  of  a  series  of  cells  is  different  from  that  of 
a  mere  row  of  metals,  for,  as  we  have  seen,  when  two 
metals  are  immersed  in  a  conducting  liquid   they  are 
thereby    equalised,    or    nearly   equalised,    in    potential. 
Hence,  if  in  the  row  of  cells  the  zincs  and  coppers  are 
all  arranged  in  one  order,  so  that  all  of  them  set  up 
electromotive -forces   in    the   same   direction,    the  total 
electromotive- force  of  the  series   will   be   equal  to   the 
electromotive -force  of  one  cell  multiplied  by  the  number 
>f  cells. 

157.  Hitherto  we    have    spoken    only    of  zinc    and 
copper  as  the  materials  for  a  battery  ;  but  batteries  may 
be  made  of  any  two  metals.     That  battery  will  have  the 

matter  is  moved  by  a  magnet  we  speak  rightly  of  magnetic  force ;  when 
electricity  moves  matter  we  may  speak  of  electric  force.  But  E.M.F.  is 
quite  a  different  thing,  not  ll  force"  at  all.  for  it  acts  not  on  matter  but  on 
electricity,  and  tends  to  move  it. 

K 


ELEMENTARY  LESSONS  ON      [CHAP.  in. 


greatest  electromotive  -force,  or  be  the  most  "intense," 
in  which  those  materials  are  used  which  give  the 
greatest  difference  of  potentials  on  contact,  or  which  are 
widest  apart  on  the  "  contact-series  "  given  in  Art.  72. 
Zinc  and  copper  are  very  convenient  in  this  respect  ; 
and  zinc  and  silver  would  be  better  but  for  the  expense. 
For  more  powerful  batteries  a  zinc-platinum  or  a  zinc- 
carbon  combination  is  preferable. 

158.  Resistance.  —  The  same  electromotive  -force 
does  not,  however,  always  produce  a  current  of  the  same 
strength.  The  strength  of  the  current  depends  not  only  on 
the  force  tending  to  drive  the  electricity  round  the  circuit, 
but  also  on  the  resistance  which  it  has  to  encounter 
and  overcome  in  its  flow.  If  the  cells  be  partly  choked 
with  sand  or  sawdust  (as  is  sometimes  done  in  so- 
called  "  Sawdust  Batteries  "  to  prevent  spilling),  or,  if  the 
wire  provided  to  complete  the  circuit  be  very  long  or 
very  thin,  the  action  will  be  partly  stopped,  and  the 
current  will  be  weaker,  although  the  E.  M.F.  may  be 
unchanged.  The  analogy  of  the  water-pipes  will  again 
help  us.  The  pressure  which  forces  the  water  through 
pipes  depends  upon  the  difference  of  level  between  the 
cistern  from  which  the  water  flows  and  the  tap  to  which 
it  flows  ;  but  the  amount  of  water  that  runs  through  will 
depend  not  on  the  pressure  alone,  but  on  the  resistance 
it  meets  with  ;  for,  if  the  pipe  be  a  very  thin  one,  01 
choked  v/ith  sand  or  sawdust,  the  water  will  only  run 
slowly  through. 

Now  the  metals  in  general  conduct  well  :  their  resist- 
ance  is  small  ;  but  metal  wires  must  not  be  too  thin  or 
loo  long,  or  they  will  resist  too  much,  and  permit  only 
a  feeble  current  to  pass  through  them.  The  liquids  in 
the  battery  do  not  conduct  nearly  so  well  as  the  metab, 
and  different  liquids  have  different  resistances.  Pure 
water  will  hardly  conduct  at  all,  and  is  for  the  feebla 
electricity  of  the  voltaic  battery  almost  a  perfect  in- 
sulator,  though  for  the  high  -potential  electricity  of  the 


CHAP,  ru.J  ELECTRICITY  AND  MAGNETISM.  131 

fi  ictional  machines  it  is,  as  we  have  seen,  a  fair  conductor. 
Salt  and  saltpetre  dissolved  in  water  are  good  con- 
ductors, and  so  are  dilute  acids,  though  strong  sul- 
phuric acid  is  a  bad  conductor.  The  resistance  of  the 
liquid  in  the  cells  may  be  reduced,  if  desired,  by  using 
larger  plates  of  metal  and  putting  them  nearer  together. 
Gases  are  bad  conductors  ;  hence  the  bubbles  of  hydro- 
gen gas  which  are  giveii  off  at  the  copper  plate  during 
the  action  of  the  cell,  and  which  stick  to  the  surface 
of  the  copper  plate,  increase  the  internal  resistance  of 
the  cell  by  diminishing  the  effective  surface  of  the  plates. 


LESSON  XIV. — Chemical  Actions  in  the  Cell. 

159.  The  production  of  a  current  of  electricity  '  '•  a 
voltaic  cell  is  always  accompanied  by  chemical  actions 
in  the  cell.     One  of  the  metals  at  least  must  be  readily 
oxidisable,  and  the  liquid  must  be  one  capable  of  acting 
on  the  metal.     As  a  matter  of  fact,  it  is  found  that  zinc 
and  the  other  metals  which  stand  at  the-electropositive 
end  of  the  contact -series  (see  Art.  72)  are  oxidisable ; 
whilst    the    electronegative    substances  —  copper,  silver, 
gold,  platinum,  and  graphite — are  less  oxidisable,  and 
the   last    three   resist   the    action  of  every  single  acid. 
There  is  no  proof  that"  their  electrical  behaviour  is  due  to 
their  chemical  behaviour  ;  nor  is  their  chemical  behaviour 
due  to  their  electrical.      Probably  both  result    from    a 
common  cause.    (See  Article  422  (bis),  and  also  p.  71.) 

160.  A  piece  of  quite  pure  zinc  when;  dipped  alone 
into  dilute  sulphuric  acid  is  not  attacked  by  the  liquid. 
But  the  ordinary  commercial  zinc  is  not  pure,  and  when 
plunged  into  dilute  sulphuric  acid  dissolves  away,  a  large 
quantity  of  bubbles  of  hydrogen  gas  being  given  off  from 
the  surface  of  the  metal.     Sulphuric  acid  is  a  complex 
substance,  in  which    every  molecule    is    made  up  of  a 
group  of  atoms, — 2  of  Hydrogen,  I  of  Sulphur,  and  4  of 


132  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

Oxygen;  or,  in  symbols,  HjSO^.  The  chemical  reaction 
by  which  the  zinc  enters  into  combination  with  the 
radical  of  the  acid,  turning  out  the  hydrogen,  is  expressed 
ra  the  following  equation  : — 

Zn     +        H2SO4          «          ZnSO4       +       H2 

Zinc      and     Sulphuric  Acid      produce    Sulphate  of  Zinc    and    Hydrogen. 

The  sulphate  of  zinc  produced  in  this  reaction  remains 
in  solution  in  the  liquid. 

Now,  when  a  plate  of  pure  zinc  and  a  plate  ot  some 
less-easily  oxidisable  metal — copper  or  platinum,  or,  best 
of  all,  carbon  (the  hard  carbon  from  the  gas  retorts) — 
are  put  side  by  side  into  the  cell  containing  acid,  no 
appreciable  chemical  action  takes  place  until  the  circuit 
is  completed  by  joining  the  two  plates  with  a  wire,  or  by 
making  them  touch  one  another.  Directly  the  circuit  is 
completed  a  current  flows  and  the  chemical  actions 
begin,  the  zinc  dissolving  in  the  acid,  and  the  acid  giving 
up  its  hydrogen  in  streams  of  bubbles.  But  it  will  be 
noticed  that  these  bubbles  of  hydrogen  are  evolved  not 
at  the  zinc  plate,  nor  yet  throughout  the  liquid,  but  at  the 
surface  of  tJie  copper  plate  (or  the  carbon  plate  if  carbon 
is  employed).  This  apparent  transfer  of  the  hydrogen 
gas  through  the  liquid  from  the  surface  of  the  zinc  plate 
to  the  surface  of  the  copper  plate  where  it  appears  is 
very  remarkable.  The  ingenious  theory  framed  by 
Grotthuss  to  account  for  it,  is  explained  in  Lesson 
XXXVIII.  on  Electro-Chemistry. 

These  chemical  actions  go  on  as  long  as  the  current 
passes.  The  quantity  of  zinc  used  up  in  each  cell  is 
proportional  to  the  amount  of  electricity  which  flows 
round  the  circuit  while  the  battery  is  at  work ;  or,  in 
other  words,  is  proportional  to  the  strength  of  the 
current.  The  quantity  of  hydrogen  gas  evolved  is  also 
proportional  to  the  amount  of  zinc  consumed,  and  also 
to  the  strength  of  the  cur-ent.  Afler  the  acid  has  thus 
dissolved  zinc  in  it,  it  will  no  longer  act  as  a  corrosive 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  133 

solvent ;  it  has  been  "  killed,"  as  workmen  say,  for  it 
has  been  turned  into  sulphate  of  zinc.  The  battery  will 
cease  to  act,  therefore,  either  when  the  zinc  has  all  dis- 
solved away,  or  when  the  acid  has  become  exhausted, 
lhat  is  to  say,  when  it  is  all  turned  into  sulphate  of  zinc. 
Stout  zinc  plates  will  last  a  long  time,  but  the  acids 
require  to  be  renewed  frequently,  the  spent  liquor  being 
emptied  out. 

161.  Local  Action. — When  the  circuit  is  not  closed 
the  current  cannot  flow,  and  there  should  be  no  chemical 
action  so  long  as  the  battery  is  producing  no  current. 
The  impure   zinc  of  commerce,  however,  does  not  re- 
main quiescent  in  the  acid,  but  is  continually  dissolving 
and  giving  off  hydrogen  bubbles.     This  local  action, 
as  it  is  termed,  is  explained  in  the  following  manner : — 
The  impurities  in  the  zinc  consist  of  particles  of  iron, 
arsenic,  and  other  metals.      Suppose  a  particle  of  iron  to 
be  on  the  surface  anywhere  and  in  contact  with  the  acid. 
It  will  behave  like  the  copper  plate  of  a  battery  towards 
the  zinc  particles  in  its  neighbourhood,  for  a  local  differ- 
ence of  potential  will  be  set  up  at  the  point  where  there 
is  metallic  contact,  causing  a  loc^l  current  to  run  from 
the  particles  of  zinc  through  the  acid  to  the  particle  of 
iron,  and  so  there  will  be  a  constant  wasting  of  the  zinc, 
both  when  the  battery  circuit  is  closed  and  when  it  is  open. 

162.  Amalgamation  of  Zinc. — We  see  now  why  a 
piece  of  ordinary  commercial  zinc  is  attacked  on  being 
placed  in  acid.     There  is  local  action  set  up  all  over  its 
surface  in  consequence  of  the  metallic  impurities  in  it. 
To   do  away  with   this    local    action,  and    abolish   the 
wasting  of  the  zinc  while  the  battery  is  at  rest,  it  is  usual 
to  amalgamate  the  surface  of  the  zinc  plates  with 
mercury.      The   surface  to  be  amalgamated  should  be 
cleaned  by  dipping  into  acid,  and  then  a  few  drops  of 
mercury  should  be  poured  over  the  surface  and  rubbed 
into  it  with   a  bit   of  linen   rag  tied  to  a  stick.     The 
mercury  unites  with  the  zinc  at  the  surface,  forming  a 


I34  ELEMENTARY  LESSONS  ON      [CHAP.  m. 

pasty  amalgam.  The  iron  particles  do  not  dissolve  in 
the  mercury,  but  float  up  to  the  surface,  whence  the 
hydrogen  bubbles  which  may  form  speedily  carry  them 
oft  As  the  zinc  in  this  pasty  amalgam  dissolves  into 
the  acid  the  film  of  mercury  unites  with  fresh  portions 
of  zinc,  and  so  presents  always  a  clean  bright  surface  to 
the  liquid. 

A  newer  and  better  process  is  to  add  about  4  per  cent  oi 
mercury  to  the  molten  zinc  before  casting  into  plates  or  rods. 
'  If  the  zinc  plates  of  a  battery  are  well  amalgamated  there  should 
be  no  evolution  of  hydrogen  bubbles  when  the  circuit"  is  open. 
Nevertheless  there  is  still  always  a  little  wasteful  local  action 
during  the  action  of  the  battery.  Jacobi  found  that  while  one 
part  of  hydrogen  was  evolved  at  the  positive  pole,  33-6  parts  oi 
zinc  were  dissolved  at  the  negative  pole,  instead  of  the  32-5 
parts  -which  are  the  chemical  equivalent  of  the  hydrogen. 

163.  Polarisation. — The  bubbles  of  hydrogen  gas 

liberated  at  the  surface  of  the  copper  plate   stick  to 

it  in  great  numbers,  and  form  a  film  over  its  surface ; 

hence  the  effective  amount  of  surface  of  the  copper  plate 

is  very   seriously  reduced   in   a   short  time.     When   a 

simple  cell,  or  battery  of  such  cells,  is  set  to  produce  a 

current,  it  is  found  that  the  strength  of  the  current  after 

a  few  minutes,  or  even   seconds,  falls  off  very  greatly, 

and    may  even    be  almost  stopped.     This   immediate 

falling  off  in  the, strength  of  the  current,  which  can  be 

observed  with  any  galvanometer  and  a  pair  of  zinc  and 

copper  plates  dipping  into  acid,  is  almost  entirely  due  to 

the  film  of  hydrogen  bubbles  sticking  to  the  copper  pole. 

A  battery  which   is  in   this   condition   is   said   to   be 

"  polarised." 

164.  Effects  of  polarisation. — The  film  of  hydro- 
gen bubbles  affects  the  strength  of  the  current  of  the  cell 
in  two  ways. 

•Firstly,  It  weakens  the  current  by  the  increased  -resist- 
ance which  it  offers  to  the  flow,  for  bubbles  of  gas  are 
bad  conductors ;  and, 

Secondly -,  It  weakens  th£  current  by  setting  up^aa 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  135 

opposing  electromotive-force;  for  hydrogen  is  almost  as 
oxidisable  a  substance  as  zinc,  especially  when  freshly 
deposited  (or  in  a  "nascent  "  state),  and  is  electropositive, 
standing  high  in  the  series  on  p.  69.  Hence  the 
hydrogen  itself  produces  a  difference  of  potential,  which 
would  tend  to  start  a  current  in  the  opposite  direction  to 
the  true  zinc-to-copper  current. 

It  is  therefore  a  very  important  matter  to  abolish  this 
polarisation,  otherwise  the  currents  furnished  by  batteries 
would  not  be  constant. 

165.  Remedies  against  Internal  Polarisation. 
— Various  remedies  have  been  practised  to  reduce  or 
prevent  the  polarisation  of  cells.  These  may  be  classed 
as  mechanical,  chemical,  and  electro-chemical. 

1.  Mechanical  Means. — If  the  hydrogen  bubbles  be 
simply  brushed  away  from  the   surface  of  the  positive 
pole,  the  resistance  they  caused  will  be  diminished.     If 
air  be  blown  into  the  acid  solution  through  a  tube,  or  if 
the  liquid  be  agitated  or  kept  in  constant  circulation  by 
siphons,  the  resistance  is  also  diminished.      If  the  surface 
be  rough  or  covered  with  points,  the  bubbles  collect  more 
freely  at  the  points  and  are  quickly  carried  up  to  the 
surface,  and  so  got  rid  of.      This  remedy  was  applied  in 
Smee's  Cell,  which  consisted  of  a  zinc  and  a  platinised 
silver  plate  dipping  into  dilute  sulphuric  acid ;  the  silver 
plate,  having  its  surface  thus  co\ered  with  a  rough  coat 
ing  of  finely  divided  platinum,  gave  up  the  hydrogen 
bubbles  freely  ;  nevertheless,  in  a  battery  of  Smee  Cells 
the  current  falls  off  greatly  after  a  few  minutes. 

2.  Chemical  Means. — If  a  highly-oxidising  substance 
be  added  to  the  acid  it  will  destroy  the  hydrogen  bubbles 
whilst  they  are  still  in  the  nascent   state,  and  thus  will 
prevent  both  the  increased  internal  resistance  and  the 
opposing    electromotive  -  force.      Such    substances    are 
bichromate  of  potash,  nitric  acid,  and  bleaching  powder 
(so-called  chloride  of  lime).     These  substances,  however, 
would  attack  the  copper  in  a  zinc-copper  cell.     Hence 


ELEMENTARY  LESSONS  ON      [CHAP.  HI. 


they  can  only  be  made  use  of  in  zinc-carbon  or  zinc- 
platinum  cells.  Nitric  acid  also  attacks  zinc  when  the 
circuit  is  open.  Hence  it  cannot  be  employed  in  the 
same  single  cell  with  the  zinc  plate.  In  the  Bichror 
mate  Battery,  invented  by  Poggendorf,  bichromate 

of  potash  is  added 
to  the  sulphuric  acid. 
This  cell  is  most  con- 
veniently made  up  as 
a  "  bottle  battery " 
(Fig.  72),  in  which  a 
plate  of  zinc  is  the  — 
pole,  and  a  pair  of 
carbon  plates,  one  on 
each  side  of  the  zinc, 
are  joined  together  at 
the  top  as  a  +  pole. 
As  this  solution  acts 
on  the  metal  zinc 
when  the  circuit  is 
open,  the  zinc  plate 
is  fixed  to  a  rod  by 


Fig.  72. 


which  it  can  be  drawn 
up  out  of  the  solution 
when  the  cell  is  not  being  worked.  Other  cases  of 
chemical  prevention  of  polarisation  are  mentioned  in 
describing  other  forms  of  battery. 

3.  Electro-chemical  Means. — It  is  possible  by  employ- 
ing double  cells,  as  explained  in  the  next  Lesson,  to  so 
arrange  matters  that  some  solid  metal,  such  as  copper, 
shall  be  liberated  instead  of  hydrogen  bubbles,  at  the 
point  where  the  current  leaves  the  liquid.  This  electro- 
chemical exchange  entirely  obviates  polarisation. 

166.  Simple  Laws  of  Chemical  Action  in  the 
Cell. — We  will  conclude  this  section  by  enumerating  the 
two  simple  laws  of  "chemical  action  in  the  cell. 

I.   The  amount  of  chemical  action  in  the  cell  is  propor~ 


CHAP.  HI.]    ELECTRICITY  AND  MAGNETISM.          137 

tiona!,  to  the  quantity  of  electricity  that  passes  through  it, 
— that  is  to  say,  is  proportional  to  the  strength  of  the 
current  while  it  passes. 

One  coulomb1  of  electricity  in  passing  through  tne  cell 
liberates  -g-^^  (or  -000010352)  of  a  gramme  of  hydro- 
gen, and  causes  ^^'^  (or  -00033644)  of  a  gramme  of 
zinc  to  dissolve  in  the  acid. 

II.  The  amount  of  chemical  action  is  equal  in  each  cell 
of  a  battery  consisting  of  cells  joined  in  series. 

The  first  of  these  laws  was  thought  by  Faraday,  who 
discovered  it,  to  disprove  Volta's  contact  theory.  He 
foresaw  that  the  principle  of  the  conservation  of  energy 
would  preclude  a  mere  contact  force  from  furnishing  a 
continuous  suppiy  of  current,  and  hence  ascribed  the 
current  to  the  chemical  actions  which  were  proportional 
in  quantity  to  it.  How  the  views  of  Volta  and  Faraday 
are  te  be  harmonised  has  been  indicated  in  the  last 
paragraph  of  Art.  72. 

LESSON  XV. —  Voltaic  Batteries. 

167.  A  good  Voltaic  Battery  should  fulfil  all  or  most 
of  the  following  conditions  : — 

1.  Its  electromotive-force  should  be  high  and  con- 

stant 

2.  Its  internal  resistance  should  be  small. 

3.  It  should  give  a  constant  current,  and  therefore 

must  be  free  from  polarisation,  and  not  liable 
to  rapid  exhaustion,  requiring  frequent  renewal 
of  the  acid. 

//   It  should  be  perfectly  quiescent  when  the  circuit 
is  open. 

5.  It  should  be  cheap  and  ol  durable  materials. 

6.  It  should  be  manageable,  and  if  possible,  should 

not  emit  corrosive  fumes. 

»  For    ths   definition  of  the   coulomb,  or   practical   unit  of  quantity  of 
electricity,  see  Art.  323. 


138  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

168.  No  single  battery  fulfils  all  these  conditions, 
however,  and  some  batteries  are  better  for  one  purpose 
and  some  for  another.  Thus,  for  telegraphing  through 
a  long  line  of  wire  a  considerable  internal  resistance  in 
the  battery  is  no  great  disadvantage  ;  while,  for  producing 
an  electric  light,  much  internal  resistance  is  absolutely 
fatal.  The  electromotive-force  of  a  battery  depends  on 
the  materials  of  the  cell,  and  on  the  number  of  cells 
linked  together,  'and  a  high  E.M.F.  can  therefore  be 
gained  by  choosing  the  right  substances  and  by  taking 
a  large  number  of  cells.  The  resistance  within  the  cell 
can  be  diminished  by  increasing  the  size  of  the  plates, 
by  bringing  them  near  together,  so  that  the  thickness 
of  the  liquid  between  them  may  be  as  small  as  possible, 
and  by  choosing  liquids  that  are  £ood  conductors.  Of 
the  innumerable  forms  of  battery  that  have  been  invented, 
only  those  of  first  importance  can  be  described.  Batteries 
may  be  classified  into  two  groups,  according  as  they 
contain  one  or  two  fluids,  or  electrolytes^ 


SINGLE-FLUID  CELL& 

169.  The  simple  cell  of  Volta,  with  its  zinc  and  copper  plates, 
has  been  already  described.  Cruickshank  suggested  to  place 
the  plates  vertically  in  a  trough,  producing  a  more  powerful 
combination.  Dr.  Wollaston  proposed  to  use  a  plate  of  copper 
of  double  size,  bent  round  so  as  to  approach  the  zinc  on  both 
sides,  thus  diminishing  the  resistance.  Smee,  as  we  have  seen, 
replaced  the  copper  plate  by  platinised  silver,  and  Walker 
suggested  the  use  of  plates  of  hard  carbon  instead  of  copper  or 
silver,  thereby  saving  cost,  and  at  the  same  time  increasing  the 
electromotive -force.  The  simple  bichromate  cell  (Fig.  72)  is 
almost  the  only  single-fluid  cell  free  from  polarisation,  and  even 
in  this  form  the  strength  of  the  current  falls  off  "after  a  few 
minutes'  working,  owing  to  the  chemical  reduction  of  the  liquid. 
Pabst  uses  an  iron-carbon  cell  with  perchloride  of  iron  as  the 
exciting  liquid.  The  iron  dissolves  and  chlorine  is  at  first 
evolved  j  but  without  polarisation  ;  the  liquid  regenerating  itself 


CHAP,  in.]     ELECTRICITY  AND  MAGNETISM. 


139 


by  absorbing  oxygen  from  the  air.  It  is  very  constant,  but  of 
low  E.  M.  F.  Complete  depolarization  is  usually  obtained  by 
two-fluid  cells,  or  by  cells  in  which  in  addition  to  the  one  fluid 
there  is  a  depolarising  solid  body,  such  as  oxide  of  manganese, 
oxide  of  copper,  or  peroxide  of  lead,  in  contact  with  the  carbon 
pole.  Such  cells  do  not  really  belong  to  the  class  of  single-fluid 
cells,  and  they  are  considered  in  the  next  group  in  which  there 
are  two  electrolytes. 

TWO-FLUID  CELLS. 

17O.  Daniell's  Battery. — Each  cell  or  "  element  " 
of  Daniell's  Battery  consists  of  an  inner  and  an  outer 
cell,  divided  by  a  porous  partition 
to  keep  the  separate  liquids  in 
the  two  cells  from  mixing.  The 
outer  cell  (Fig.  73)  is  usually  of 
copper,  and  serves  also  as  a 
copper  plate.  Within  it  is  placed 
a  cylindrical  cell  of  unglazed 
porous  porcelain  (a  cell  of  parch- 
ment, or  even  of  brown  paper, 
will  answer),  and  in  this  is  a 
rod  of  amalgamated  zinc  for  the 
negatne  pole.  The  liquid  in 
the  inner  cell  is  dilute  sulphuric 
acid ;  that  in  the  outer  cell  is  a  saturated  "solution  of 
sulphate  of  copper  ("  blue  vitriol  "),  some  spare  crystals 
of  the  same  substance  being  contained  in  a  perforated 
shelf  at  the  top  of  the  cell,  in  order  that  they  may 
dissolve  and  replace  that  which  is  used  up  while  the 
battery  is  in  action. 

When  the  circuit  is  closed  the  zinc  dissolves  in  the  dilute 
acid,  forming  sulphate  of  zinc,  and  liberating  hydrogen  gas  ;  but 
this  gas  does  not  appear  in  bubbles  on  the  surface  of  the  copper 
cell,  for,  since  the  inner  cell  is  porous,  the  molecular  actions 
(by  which  the  freed  atorris  of  hydrogen  are,  as  explained  by 
Fig.  155,  handed  on  through  the  acid)  traverse  the  pores  of  the 
inner  cell,  and  there,  in  the,  solution  of  sulphate  of  cooper,  the 


Mo  ELEMENTARY  LESSONS  ON       [CHAP.  lit 

hydrogen  atoms  are  exchanged  for  copper  atoms,  the  result 
being  that  pure  copper,  and  not  hydrogen  gas,  is  deposited 
on  the  outer  copper  plate.  Chemically  these  actions  may  be 
represented  as  taking  place  in  two  stages. 

Zn         +       IIa  SO4  =  Zn  SO4  +         H2 

Zinc        and    Sulphuric  Acid    produce    Sulphate  of  Zinc    and    Hydrogen. 

And  then 

H,       {-  Cu  SO4  =  H2  SO4        +       Cu. 

Hydrogen  and  Sulphate  of  Copper  produce  Sulphuric  Acid  and    Copper 

The  hydrogen  is,  as  it  were,  translated  electro-chemically  into 
copper  during  the  round  of  changes,  and  so  while  the  zinc  dis- 
solves away  the  copper  grows,  the  dilute  sulphuric  acid  gradually 
changing  into  sulphate  of  zinc,  and  the  sulphate  of  copper  into 
sulphuric  acid.  There  is  therefore  no  polarisation  so  long  as 
the  copper  solution  is  saturated  ;  and  the  battery  is  very 
constant,  though  not  so  constant  in  all  cases  as  Clark's  standard 
cell  described  in  Art  177,  owing  to  slight  variations  in  the 
electromotive-force  as  the  composition  of  the  other  fluid  varies. 
When  sulphuric  acid  diluted  with  twelve  parts  of  water  is  used 
the  E.M.F.  is  1-181  (legal)  volts.  The  E.M.F.  is  1-047  volts 
when  concentrated  zinc  sulphate  is  used;  i-cy  volts  w3.cn 
a  half-concentrated  solution  of  zinc  sulphate  is  used  ;  and,  in 
the  common  cells  made  up  with  water  or  dilute  acid,  i  '028 
volts  or  less.  Owing  to  its  constancy,  this  battery,  made 
up  in  a  convenient  flat  form  (Fig.  77)»  has  been  much  used 
m  telegraphy. 

171.  Grove's  Battery. — Sir  Wm.  Grove  devised  a 
form  of  batter)-  having  both  greater  E.M.F.  and  smaller 
internal  resistance  than  Daniell's  Cell.  In  Grove's 
element  there  is  an  outer  cell  of  glazed  ware  or  of 
ebonite,  containing  the  amalgamated  zinc  plate  and 
dilute  sulphuric  acid.  In  the  inner  porous  cell  a  piece 
of  platinum  foil  serves  as  the  negative  pole,  and  it  dips 
into  the  strongest  nitric  acid.  There  is  no  polarisation 
in  this  cell,  for  the  hydrogen  liberated  by  the  solution  of 
the  zinc  in  dilute  sulphuric  acid,  in  passing  through  the 


CHAP.  HI.]    ELECTRICITY  AND  MAGNETISM.  141 

nitric  acid  in  order  to  appear  at  the  platinum  pole,  de- 
composes the  nitric  acid  and  is  itself  oxidized,  producing 
water  and  the  red  fumes  of  nitric  peroxide  gas.  This 
gas  does  not,  however,  produce  polarisation,  for  as  it  is 
very  soluble  in  nitric  acid  it  does  not  form  a  film  upon 
the  face  of  the  platinum  plate,  nor  does  it,  like  hydrogen, 
set  up  an  opposing  electromotive -force  with  the  zinc. 
The  Grove  cells  may  be  made  of  a  flat  shape,  the  zinc 
being  bent  up  so  as  to  embrace  the  flat  porous  -  cell  on 
both  sides.  This  reduces  the  internal  resistance,  which 
is  already  small  on  account  of  the  good  conducting 
powers  of  nitric  acid.  Hence  the  Grove's  cell  will 
furnish  for  three  or  four  hours  continuously  a  powerful 
current.  The  E.M.F.  of  one  cell  is  about  1-9  volts.  A 
single  cell  will  readily  raise  to  a  bright  red  heat  two  or 
three  inches  of  thin  platinum  wire,  or  drive  a  small 
electro -magnetic  engine.  For  producing  larger  effects 
a  number  of  cells  must  be  joined  up  "  in  series,"  the 
platinum  of  one  cell  being  clamped  to  the  zinc  of  the 
next  to  it.  Fifty  such  cells,  each  holding  about  a  quart 
of  liquid,  amply  suffice  to  produce  an  electric  light,  as 
will  be  explained  in  Lesson  XXXII. 

172.  Bunsen's  Battery. — The;  battery  which  bears 
Bunsen's  name  is  a  modification  of  that  of  Grove,  and 
was  indeed  originally  suggested  by  him.  In  the  Bunsen 
cell  the  expensive1  platinum  foil  is  replaced  by  a  rod  or 
slab  of  hard  gas  carbon.  The  difficulty  of  cutting  this 
into  thin  slabs  causes  a  cylindrical  form  of  batter}',  with 
a  rod  of  carbon,  as  shown  in  Fig.  74,  to  be  preferred  to 
the  flat  form.  The  difference  of  potentials  for  a  zinc- 
carbon  combination  is  a  little  higher  than  for  a  zinc- 
platinum  one,  which  is  an  advantage  ;  but  the  Bunsen 
cell  is  troublesome  to  keep  in  order,  and  there  is  some 
difficulty  in  making  a  good  contact  between  the  rough 

1  Platinum  costs  about  30  shillings  an  ounce — nearly  half  as  much  as  gold  ; 
while  a  hundredweight  of  the  gas  carbon  may  be  had  for  a  mere  trifle,  often 
for  nothing  more  than  the  cost  of  carrying  it  from  the  gasworks 


142 


ELEMENTARY  LESSONS  ON     [CHAP.  in. 


surface  of  the  carbon  and  the  copper  str?.p  which 
connects  the  carbon  of  one  cell  to  the  zinc  of  the  next. 
Fig.  75  shows  the  usual  way  of 
coupling  up  a  series  of  five  such 
cells.  The  Bunsen's  battery  will 
continue  to  furnish  a  current  for 
a  longer  time  than  the  flat 
Grove's  cells,  on  account  of  the 
larger  quantity  of  acid  contained 
by  the  cylindrical  pots.1 

173.  Leclanche's  Battery : 
Niaudet's  Battery. — For  work- 
ing electric  bells  and  telephones, 
and  also  to  a  limited  extent  in 
telegraphy,  a  zinc-carbon  cell  is 
employed,  invented  by  Mons. 
Leclanche',  in  which  the  exciting  liquid  is  not  dilute 
acid,  but  a  solution  of  salammoniac.  In  this  the  zinc 
dissolves,  forming  a  double  chloride  of  zinc  and  am- 
monia, while  ammonia ^gas  and  hydrogen  are  liberated 


74. 


Fig.  75. 

at  the  Carbon  pole."  To  prevent  polarisation  the  carbon 
plate   is   packed   inside  a  porous  pot   along   with  frag- 

1  Gallon  constructed  a  large  battery  in  which  cast-iron  formed  the  positive 
pole,  being  immersed  in  strong  nitric  acid,  the  zincs  dipping  into  dilute  acid. 
The  iron  under  these  circumstances  is  not  acted  upon  by  the  acid,  but 
assumes  a  so-called  "passive  .state."  In  this  condition  its  surface  appear* 
to  be  impregnated  with  a  film  of  magnetic  peroxide,  or  of  oxygen. 


CHAP,  in.]  ^ELECTRICITY  AND  MAGNETISM.  143 

ments  of  carbon  and  powdered  binoxide  of  manga- 
nese, a  substance  which  slowly  yields  up  oxygen  and 
destroys  the  hydrogen"  bubbles.  If  used  to  give  a 
continuous  current  for  many  minutes  together,,  the 
power  of  the  cell  falls  off  owing  to  the  accumulation  of 
the  hydrogen  bubbles  ;  but  if  left  to  itself  for  a  time  the 
cell  recovers  itself,  the  binoxide  gradually  destroying  the 
polarisation.  As  the  cell  is  in  other  respects  perfectly 
constant,  and  does  not  require  renewing  for  months  or 
years,  it  is  well  adapted  for  domestic  purposes.  Three 
Leclanche'  cells  are  shown  joined  in  series,  in  Fig.  76. 


Fig.  76. 

In  more  recent  forms  the  binoxide  of  manganese  is 
applied  in  a  conglomerate  attached  to  the  face  of  the 
carbon,  thus  avoiding  the  necessity  of  using  a  porous 
inner  cell. 

Mons.  Niaudet  has  also  constructed  a  zinc -carbon  cell  in 
which  the  zinc  is  placed  in  a  solution  of  common  salt  (chloride 
of  sodium),  and  the  carbon  is  surrounded  by  the  so-called 
chloride-of-lime  (or  bleaching-powder),  which  readily  gives  up 
chlorine  and  oxygen,  both  of  which  substances  will  destroy  the 
hydrogen  bubbles  and  prevent  polarisation.  This  cell  has  a 
higher  E.M.F.  and  a  less  resistance  than  the  Leclanche.  De 
Lalande  and  Chaperon  propose  a  cell  in  which  oxide  of  copper 
is  used  as  a  solid  depolariser  in  a  solution  of  caustic  potash. 

174.  De  la  Rue's  Battery. — Mr.  De  la  Rue  has 
constructed  a  perfectly  constant  cell  in  which  zinc  and 


144  ELEMENTARY  LESSONS  ON       [CHAP,  in 

silver  are  the  two  metals,  the  zinc  being  immersed  in 
chloride  of  zinc,  and  the  silver  embedded  in  a  stick  oi 
fused  chloride  of  silver.  As  the  zinc  dissolves  away, 
metallic  silver  is  deposited  upon  the  +  pole,  just  as  the 
copper  is  in  the  DanielPs  cell.  Mr.  De  la  Rue  has  con- 
structed an  enormous  battery  of  over  11,000  little  cells. 
The  difference  of  potential  between  the  first  zinc  and 
last  silver  of  this  gigantic  battery  was  over  1 1,000  volts, 
yet  even  so  no  spark  would  jump  from  the  +  to  the  — 
pole  until  they  were  brought  to  within  less  than  a  quarter 
of  an  inch  of  one  another.  With  8040  cells  the  length 
of  spark  was  only  0*08  of  an  inch. 

175.  Marie"  Davy's  Battery. — in  this  cell  the  zinc 
dips  into  sulphate  of  zinc,  while  a  carbon  plate  dips  into 
a  pasty  solution  of  mercurous  sulphate.  When  the  cell 
is  in  action  mercury  is  deposited  on  the  surface  of  the 
carbon,  so  that  the  cell  is  virtually  a  zinc-mercury  cell. 
It  was  largely  used  for  telegraphy  in  France  before  the 
introduction  of  the  Leclanchd  cell. 

178.  Gravitation  Batteries. — Instead  of  employing 
a  porous  cell  to  keep  the  two  liquids  separate,  it  is  pos- 
sible, where  one  of  the  liquids  is  heavier  than  the  other, 
to  arrange  that  the  heavier  liquid  shall  form  a  stratum 
at  the  bottom  of  the  cell,  the  lighter  floating  upon  it. 
Such  arrangements  are  called  gravitation  batteries;  but 
the  separation  is  never  perfect,  the  heavy  liquid  slowly 
diffusing  upwards.  Daniell's  cells  arranged  as  gravi- 
tation batteries  have  been  contrived  by  Meidinger, 
Minotto,  Callaud,  and  Sir.  W.  Thomson.  In  Siemens' 
modification  of  Daniell's  cell  paper -pulp  is  used  to 
separate  the  two  liquids.  The  "  Sawdust  Battery "  of 
Sir  W.  Thomson  is  a  Daniell's  battery,  having  the 'cells 
filled  with  sawdust,  to  prevent  spilling  and  make  them 
portable. 

177.  Latimer  Clark's  Standard  Cell. — A  standard 
cell  whose  E.M.F.  is  even  more  constant  than  that  of 
the  Daniel!  was  suggested  by  Latimer  Clark.  This 


CHAP,  in.]    ELECTRICITY  AND  MAGNETISM. 


'45 


battery  is  composed  of  pure  mercury,  on  which  floats  a 
paste  of  mercurous  sulphate,  a  plate  of  zinc  resting  on 
the  paste.  Contact  with  the  mercury,  which  acts  as 
the  positive  pole,  is  made  with  a  platinum  wire.  The 
E.M.F,  is  i  -4  3  6  legal  volts. 

178.  The  following  table  gives  the  electromotive-forces 
of  the  various  batteries  enumerated  : — 


Name  of  Battery,  etc. 


E.M.F.  in  (legal)  Volts. 


Single-Fluid  Cells. 

Volta  (Wollaston,  etc.) 
Smee        ..... 
Poggendorff  (Grenet,  Trouve, 
etc.)       .... 
Pabst         .... 

Two-Fluid  Cells. 
Daniell  (Meidinger,  Minotto, 

Thomson,  etc.) 
Grove  ... 
Bunsen      .... 
Leclanche 

Nia'udet     .... 
Lalande  and  Chaperon 
De  la  Rue          .         . 
Marie  Davy        .          , 
Latimer  Clark  (Standard)    . 

Secondary  Batteries. 
Ritter 
Plante  (Faure,  Sellon,  etc.) 


1-036 — 0-81 
0-64        ? 

2-27—17.7 
078 


1-122 — I  -07 — I  -047  —  I  -028 

1-934— 176 
1-942—173 

I -59  — 1-46 — 1-402 

1-63 

0-66 

1-046 

1-50 

••436 


2-22 — 1-47 
2'22  — 1-96 


179.  Strength  of  Current. — The  student  must  not 
mistake  the  figures  given  in  the  above  table  for  the 
strength  of  current  which  the  various  batteries  will 
yield;  that  depends,  as  was  said  in  Lesson  XIII.,  on 
the  internal  resistance  of  the  cells  as  well  as  on  their 
E.M.F.  The  E.M.F.  of  a  cell  is  independent  of  its 
size,  and  is  determined  solely  by  the  materials  chosen 
and  their  condition.  The  resistance  depends  on  the 

L 


146  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

size  of  the  cell,  the  conducting  qualities  of  the  liquid, 
the  thickness  of  the  liquid  which  the  current  must 
traverse,  etc. 

The  exact  definition  of  the  strength  of  a  current  is 
as  follows  :  The  strength  of  a  current  is  the  q^lantity  oj 
electricity  which  flows  past  any  point  of  the  circuit  in  one 
second?-  Suppose  that  during  10  seconds  25  coulombs 
of  electricity  flow  through  a  circuit,  then  the  average 
strength  of  that  strong  current  during  that  time  has  been 
2^  coulombs  per  second,  or  2|  amperes.  The  usual 
strength  of  currents  used  in  telegraphing  over  main 
lines  is  only  from  five  to  ten  thousandths  of  an  ampere. 

If  in  /  seconds  a  quantity  of  electricity  Q  has  flowed 
through  the  circuit,  then  the  strength  C  of  t  the  current 
during  that  time  is  represented  by  the  equation  : 

C.9. 

Moreover,  if  C  represents  the  strength  of  the  current, 
the  total  quantity  of  electricity  that  has  passed  through 
the  circuit  in  a  given  time,  /  is  found  by  multiplying  the 
strength  of  the  current  by  the  time  ;  or 

Q»G* 

For  the  quantity  of  electricity  that  is  thus  transferred 
will  be  proportional  to  the  strength,  of  the  flow,  and  to 
the  time  that  it  continues. 

The  laws  which  determine  the  strength  of  a  current 
in  a  circuit  were  first  enunciated  by  Dr.  G.  S.  Ohm,  who 
stated  them  in  the  following  lavv : 

18O.  Ohm's  Law.  —  The  strength  of  the  curient 
•varies  directly  as  the  electromotive -force,  and  inversely 

1  The  terms  "strong,"  "great,"  and  ''intense,"  as  applied  to  current?, 
mean  precisely  the  same  thing.  Formerly,  before  Ohm's  Law  was  ^properly 
understood,  electricians  used  to  talk  about  "quantity  currents,"  and 
"intensity  currents,"  meaning  by  the  former  term  a  current  flowing  through 
a  circuit  in  which  there  is  very  small  resistance  inside  the  battery  or  out  : 
and  by  the  latter  expression  they  designated  a  current  due  to  a  high  electro- 
motive-force The  terms  were  convenient,  but  should  be  avoided  as  mis- 
leading. 


CHAP.  HI.]   ELECTRICITY  AND  MAGNETISM.  147 

as  the  resistance  of  the  circuit ;  or,  in  other  words,  any- 
thing that  makes  the  E.M.F.  of  the  cell  greater  will 
increase  the  strength  of  the  current,  while  anything  that 
increases  the  resistance  (either  the  internal  resistance  in 
the  cells  themselves  or  the  resistance  of  the  external 
wires  of  the  circuit)  will  dimmish  the  strength  of  the 
current.  (See  further  concerning  Ohm's  Law  m  Lesson 
XXIX.) 

Now  the  internal  resistances  of  the  cells  we  have 
named  differ  very  greatly,  and  differ  with  their  size. 
Roughly  speaking  We  may  say  that  the  resistance  in  a 
DanielPs  cell  is  about  five  times  that  in  a  Grove's  cell  of 
equal  size.  The  Grove's  cell  has  therefore  both  a 
higher  E.M.F.  and  less  internal  resistance.  It  would 
in  fact  send  a  current  about  eight  times  as  strong  as 
the  Darnell's  cell  of  equal  size  through  a  short  stout 
wire. 

181.  We  may  then  increase  the  strength  of  a  battery 
in  two  ways  : — 

(1)  by  increasing  its  E.M.F 

(2)  by  diminishing  its  internal  resistance. 

The  electromotive -force  of  a  cell  being  determined 
by  the  materials  of  which  it  is  made,  the  only  way  to 


Fig.  77. 

increase  the  total  E.M.F.  of  a  battery  of  given  materials 
is  to  increase  the  number  of  cells  joined  in  series.     It  is 


148  ELEMENTARY  LESSONS  ON      [CHAP.  iti. 

frequent  in  the  telegraph  service  to  link  thus  together 
two  or  three  hundred  of  the  flat  DanielPs  cells ;  and 
they  are  usually  made  up  in  trough-like  boxes,  containing 
a  series  of  10  cells,  as  shown' in  Fig.  77. 

To  diminish  the  internal  resistance  of  a  cell  the  follow- 
ing expedients  may  be  resorted  to  : — 

(i.)  The  plates  may  be  brought  nearer  together,  so 
that  the  current  shall  not  have  to  traverse  so  thick  a 
stratum  of  liquid. 

(2.)  The  size  of  the  plates  may  be  increased,  as  this 
affords  the  current,  as  it  were,  a  greater  number  of 
possible  paths  through  the  stratum  of  liquid. 

(3.)  The  zincs  of  several  cells  may  be  joined  together, 
to  form,  as  it  were,  one  large  zinc  plate,  the  coppers 
being  also  joined  to  form  one  large  copper  plate.  Cells 
thus  joined  are  said  to  be  united  "  in  parallel  circuit," 
or  "  for  quantity,"  to  distinguish  this  method  of  joining 
from  the  joining  in  simple  series.  Suppose  four  similar 
cells  thus  joined,  the  current  has  four  times  the  available 
number  of  paths  by  which  it  can  traverse  the  liquid 
from  zinc  to  copper  ;  hence  the  internal  resistance  of  the 
whole  will  be  only  ^  of  that  of  a  single  cell.  But  the 
E.M.F.  of  them  will  be  no  greater  thus  than  that  of 
one  cell. 

It  is  most  important  for  the  student  to  remember  that 
the  strength  of  the  current  is  also  affected  by  the  resist- 
ances of  the  wires  of  the  external  circuit ;  and  if  the 
external  resistance  be  already  great,  as  in  telegraphing 
through  a  long  line,  it  is  little  use  to  diminish  the  internal 
resistance  if  this  is  already  much  smaller  than  the  resist- 
ance of  the  line  \\ire. 

The  E.M.F.  of  the  single-fluid  cells  of  Volta  and  Smee 
is  marked  as  doubtful,  for  the  opposing  E.M.F.  of  polar- 
isation sets  in  almost  before  the  true  E.M.F.  of  the  cell 
can  be  measured.  The  different  values  assigned  to  other 
cells  are  accounted  for  by  the  different  degrees  of  con- 
centration of  the  liquids.  Thus  in  the  Daniell's  cells 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM.  149 

used  in  telegraphy,  water  only  is  supplied  at  first  in  the 
cells  containing  the  zincs  ;  and  the  E.M.F.  of  these  is  less 
than  if  acid  or  sulphate  of  zinc  were  added  to  the  water. 

182. — Other  Batteries. — Numerous  other  forms  of  battery 
have  been  suggested  by  different  electricians.  There  are  three, 
of  theoretical  interest  only,  in  which  the  electromotive-foice  is 
due,  not  to  differences  of  potential  at  the  contact  of  dissimilar 
metals,  but  to  differences  of  potential  at  the  contact  of  a  metal 
or  metals  with  liquids.  The  first  of  these  was  invented  l>y  the 
Emperor  Napoleon  III.  Both  plates  were  of  copper,  dipping 
respectively  into  solutions  of  dilute  sulphuric  acid  and  of 
caustic  soda,  separated  by  a  porous  cell.  The  second  of  these 
combinations,  due  to  NYohler,  employs  plates  of  aluminium  only, 
dipping  respectively  into  strong  nitric  acid  and  a  solution  of 
caustic  soda.  In  the  third,  invented  by  Dr.  Fleming,  the  two 
liquids  do  not  even  touch  one  another,  being  joined  together  by 
a  second  metal.  In  this  case  the  liquids  chosen  are  sodium 
persulphide  and  nitric  acid,  and  the  two  metals  copper  and  lead. 
A  similar  battery  might  be  made  with  copper  and  zinc,  using 
solutions  of  ordinary  sodium  sulphide,  and  dilute  sulphuric  acid 
in  alternate  cells,  a  bent  zinc  plate  dipping  into  the  first  and 
second  cells,  a  bent  copper  plate  dipping  into  second  and  third, 
and  so  en ;  for  the  electromotive  -  force  of  a  copper  -  sodium 
sulphide-zinc  combination  is  in  the  reverse  direction  to  that  of  a 
copper-sulphuric  acid-zinc  combination. 

Bennett  has  lately  described  a  cheap  and  most  efficient  battery, 
in  which  the  metals  are  iron  and  zinc,  and  the  exciting  liquid  a 
strong  solution  of  caustic  soda.  Old  meat-canisters  packed  with 
iron  filings  answer  well  for  the  positive  element,  and  serve  to 
contain  the  solution.  Scrap  zinc  thrown  into  mercury  in  a 
shallow  inner  cup  of  porcelain  forms  the  negative  pole. 

Skrivanoff  has  modified  the  zinc-carbon  cell  of  Latimer  Clark, 
by  employing  a  stiff  paste  made  of  ammonio-mercuric  chloride 
and  common  salt,  thereby  rendering  the  cells  dry  and  portable. 

Jablochkoff  has  described  a  batter)'  in  which  plates  of  carbon 
and  iron  are  placed  in  fused  nitre  ;  the  carbon  is  here  the 
electro-positive  element,  being  rapidly  consumed  in  the  liquid. 

Plante's  and  Faure's  Secondary  Batteries,  and  Grove's 
Gas  Battery,  are  described  in  Arts.  415,  416. 

The  so-called  Dry  Pile  of  Zamboni  deserves  notice. 
It  consists  of  a  number  of  paper  discs,  coated  with  zinc- 


150  ELEMENTARY  LESSONS  ON      [CHAP,  ill 

foil  on  one  side  and  with  binoxide  of  manganese  on  the 
other,  piled  upon  one  another,  to  the  number  of  some 
thousands,  in .  a  glass  tube.  Its  internal  resistance  is 
enormous,  as  the  internal  conductor  is  the  moisture  of 
the  paper,  and  this  is  slight ;  but  its  electromotive-force 
is  very  great,  and  a  good  dry  pile  will  yield  sparks. 
Many  years  may  elapse  before  the  zinc  is  completely 
oxidised  or  the  manganese  exhausted.  In  the  Clarendon 
Laboratory  at  Oxford  there  is  a  dry  pile,  the  poles  of 
which  are  two  metal  bells :  between  them  is  hung  a 
small  brass  ball,  which,  by  oscillating  to  and  fro,  slowly 
discharges  the  electricity.  It  has  now  been  continuously 
ringing  the  bells  for  over  forty  years. 

183.  Effect  of  Heat  on  Batteries.— -If  a  cell  be 
warmed  it  yields  a  stronger  current  than  when  cold. 
This  is  chiefly  due  to  the  fact  that  the  liquids  conduct 
better  when  warm,  the  internal  resistance  being  thereby 
reduced.  A  slight  change  is  also  observed  in  the  E.M.F. 
on  heating ;  thus  the  E.M.F.  of  a  Daniell's  cell  is  about 
l£  per  cent  higher  when  warmed  to  the  temperature  of 
boiling  water,  while  that  of  a  bichromate  battery  falls  off 
nearly  2  per  cent  under  similar  circumstances. 


LESSON  XVI. — Magnetic  Actions  of  the  Current. 

184.  About  the  year  1802  Romagnosi,  of  Trente, 
discovered  that  a  voltaic  pile  affects  a  magnetised 
needle,  and  causes  it  to  turn  aside  from  its  usual  posi- 
tion. The  discovery,  however,  dropped  into  oblivion, 
having  never  been  published.  A  connection  of  some 
kind  between  magnetism  and  electricity  had  long  been 
suspected.  Lightning  had  been  known  to  magnetise 
knives  and  other  objects  of-  steel;  but  almost  all 
attempts  to  imitate  these  effects  by  powerful  charges  of 
electricity,  or  by  sending  currents  of  electricity  through 


CHAP.  III.]   ELECTRICITY  AND  MAGNETISM. 


steel  bars,  had  failed.1  The  true  connection  between 
magnetism  and  electricity  remained  to  be  discovered. 

In  1819,  Oerstedt,  of  Copenhagen,  showed  that  a 
magnet  tends  to  set  itself  at  right-angles  to  a  wire  carry- 
ing an  electric  current.  He  also  found  that  the  way  in 
which  the  needle  turns,  whether  to  the  right  or  the  left 
of  its  usual  position,  depends  upon  the  position  of  the 
wire  that  carries  the  current — whether  it  is  above  or 
below  the  needle, — and  on  the  direction  in  which  the 
current  flows  through  the  wire. 

185.  Oerstedt's  Experiment. — Very  simple  appar- 
atus suffices  to  repeat  the  fundamental  experiment.  Let 
a  magnetic  needle  be  suspended  on  a  pointed  pivot,  as 
in  Fig.  78.  Above  it,  and  parallel  to  it,  is  held  a  stout 


Fig.  78. 

copper  wire,  one  end  of  which  is  joined  to  one  pole  of  a 
battery  of  one  or  two  cells.  The  other  end  of  the  wire 
is  then  brought  into  contact  with  the  other  pole  of  the 
battery.  As  soon  as  the  circuit  is  completed  the  current 
flows  through  the  wire  and  the  needle  turns  briskly  aside. 
If  the  current  be  flowing  along  the  wire  above  the  needle 

1  Down  to  this  point  in  these  lessons  there  has  been  no  connection  between 
magnetism  and  electricity,  though  something  has  been  said  about  each.  The 
student  who  cannot  remember  whether  a  charge  of  electricity  does  or  does 
not  affect  a  magnet,  should  turn  back  to  what  was  said  in  Art  91. 


152  ELEMENTARY  LESSONS  ON      [CHAP.  ill. 

*.         i  "  •  ' 

in  the  direction  from  north  to  south,  it  will  cause  the 
N.-  seeking  end  of  the  needle  to  turn  eastwards  :  if  the 
current  flows  from  south  td  north  in  the  wire  the  N.-seek- 
ing  end  of  the  needle  wjll  be  deflected  westwards.  If 
the  wire  is,  however,  below  the  needle,  the  motions  will 
be  reversed,  and  a  current  flowing  from  north  to  south 
will  cause  the  N. -seeking  pole  to  turn  westwards. 

186.  Amp&re's   Rule.  —  To  keep  these  movements 
in  memory,  Ampere  suggested  the  following  fanciful  but 
useful  rule.  -   Siippose  a  man  swimming  in  the  wire  with 
the,  ctfrrent,  and  that  he  turns  so  as  to  face  the  needle,  then 
the  N. -seeking  pole  of  the  neisdle  will  be  deflected  towards 
his  left  hand.      In  other  words,  the  deflection  of  the 
Mi-seeking  pole  of  a*  magnetic  needle,  as  viewed  from 
the  conductor,  is  towards  the  left  of  the  current. 

For  certain  particular  cases  in  which  a  fixed  magnet  pole  acts 
on  a  movable  circuit,  the  following  converse  to  Amperes  Rule 
will  be  found  convenient.  Suppose  a  man  swimming  in  the 
wire  with  the  current,  'and  that  he  turns  so  as  to  look  along  the 
direction  of  tfte  lines  of  force  of -the  pole  (i.e.  as  the  lines  of 
fo?ce  run,  from  the  pole  if  it  be  N.  -seeking,  towards  the  pole  if  it 
be  S.  -seeking),  then  he  and  the  conducting  wire  with  him  will  be 
urged  toward  his  left, 

187.  A  little  consideration  will  show  that  if  a  current 

be  carried  below  a  needle  in  one  direc- 
tion, and  tnen  back  in  the  opposite 
direction  above  the  needle,  by  bending 
the  wire  round,  as  in  Fig.  79,  the 
forces 'exerted  on  the  needle  by  both 
portions  of  the  current  will  be  in  the 
same  direction.  For  let  a  be  the 
N. -seeking,  and  b  the  S. -seeking,  pole 
of  the  suspended  needle,  then  the 
g.  79.  tendency  of  the  .current  in  the  lower 

part  of  the 'wire  will  be  to  turn  the 
needle  so  that  a  comes  towards  the  observer,  while  b. 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM.  153 

retreats  ;  while  the  current  flowing  above,  which  also 
deflects  the  N.-seeking  pole  to  'its  left,  will  equally  urge 
a  towards  the  observer,  and  b  from  him.  The  needle 
will  not  stand  out '  completely  at  right -angles  to  the 
direction  of  the  "wire  conductor,  but  will  take  an  oblique 
position.  The  directive  forces  of  the  earth's  magnetism 
are  tending  to  make  -the  needle  point  north-and-south. 
The  electric  current  is  acting  on  the  needle,  tending 
to  make  it  set  .itself  west -and -east.  The  resultant 
force  will  .be  in  an '  oblique  direction  between  these, 
and'Will  depend  upon -the  relative  strength"  of  the  two 
conflicting  forces.  If  the  current  is  very  strong  the 
needle  wilMurn  widely  round  ;  but  could  only  turn  com- 
pletely  to  a  right-angle  if  the  current  were  infinitely  strong 
If,  however,  the  current  is  feeble  in  comparison  with  the 
directive  magnetic  force,  the  needle  will  turn  very  little. 
188.  This  arrangement  will,  therefore,  serve  roughly 
as  §L  G-alvanoscope  or  indicator  of  currents  ;  for  the 
movement  of  the  needle  shows  the  direction  of  the 
current,  and  indicates  whether  it  is  a  strong  or  a  weak 
one.  This  apparatus  is  too  rough  to  detect  very  delicate 
currents.  To.  6btain  a  more  sensitive  instrument  there 
are  Jwo  possible  courses  :  (/.).  Increase  the  effective 
action  of  the  current  by  carrying  the  wire  more  than 
once  Around  the  needle  :  (/;.)  Decrease  the  opposing 
directive  force  of  the -earth's  magnetism  by  some  com- 
pensating contrivance. 

1S9'.  Sch-weigger's    Multiplier.  —  The  first  of  the 
above  suggestions  was  carried  out  by  Schweigger,  who 
constructed  a  ijiultiplier  of  many  turns  of  wire.     A  suit- 
able''frame 'of  wood,,  brass,  or  ebonite,  is  prepared  to 
receive  the  wire,  which  must  be  "  insulated,"  or  covered 
•with    silk,    of    cotton,   or  guttapercha,    to    prevent    the 
.'separate  turns  of  the  coil  from  coming  into  contact  with 
each  other.     Within  this  frame,  which  may  be  circular, 
elliptical,  or  more  usually  rectangular,  as  in  Fig.  80,  the 
needle  is  suspended,  the  frame  being  placed  so  that  the 


154  ELEMENTARY  LESSONS  ON      ICHAP.  in. 

wires  lie  in  the  magnetic  meridian.      The  greater  the 

number  of  turns  the  more 
powerful  will  be  the  mag- 
netic deflection  produced 
by  the  passage  of  equal 
quantities  of  current.  But 
if  the  wire  is  thin,  or  the 
number  of  turns  of  wire 
numerous,  the  resistance 
thereby  offered  to  the  flow 
of  electricity  may  very 
greatly  reduce  the  strength 
of  the  current.  The  student 
will  grasp  the  importance 

of  this  observation  when  he  has  read  the  chapter  on 
Ohm's  Law. 

19O.  Astatic  Combinations. — The  directive  force 
exercised  by  the  earth's  magnetism  on  a  magnetic  needle 
may  be  -reduced  or  obviated  by  one  of  two  methods  : — 

(a.)  By  employing  a  compensating  magnet.  An  ordinary 
long  bar  magnet  laid  in  the  magnetic  meridian,  but  with 
its  N. -seeking  pole"  directed  towards  the.  north,  will,  if 
placed  horizontally  above  or  below  a  suspended  magnetic 
needle,  tend  to  make  the  needle  set  itself  with  its  S.-seek- 
ing  pole  northwards.  If  near  the  needle  it  may  over- 
power the  directive  force  of  the  earth,  and  cause  the 
needle  to  reverse  its  usual  position.  If  it  is  far  away,  all 
it  can  do  is  *o  lessen  the  directive  force  of  the  earth. 
At  a  certain  distance  the  magnet  will  just  compensate 
this  force,  and  the  needle  will  be  neutral.  This  arrange- 
ment for  reducing  the  earth's  directive  force  is  applied 
in  the  reflecting  galvanometer  shown  in  Fig.  91,  in 
which  the  magnet  at  the  top,  curved  in  form  and  capable 
of  adjustment  to  any  height,  affords  a  means  of  adjust- 
ing the  instrument  to  the  desired  degree  of  sensitiveness 
by  raising  or  lowering  it. 

(b.)  By  using  an  astatic  pair  of  magnetic  needles. 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM. 


155 


If  two  magnetised  needles  of  equal  strength  and  size  are 

bound  together  by  a  light  wire  of  brass,  or  aluminium, 

in    reversed    positions,    as 

shown  in  Fig.  81,  the  force 

urging  one  to  set  itself  in 

the    magnetic    meridian    is 

exactly  counterbalanced  by 

the  force  that   acts  on  the 

other.       Consequently   this 

pair  of  needles  will  remain 

in  any  position  in  which  it  is 

set,  and  is  independent  of  the 

earth's  magnetism.     Such  a 

combination  is  known  as  an 

astatic  pair.     It  is,  however,  difficult  in  practice  to 

obtain  a  perfectly  astatic  pair,  since  it  is  not  easy  to 

magnetise  two  needles  exactly  to  equal  strength,  nor  is 

it  easy  to  fix  them  perfectly  parallel  to  one  another. 
Such  an  astatic  pair  is,  however, 
readily  deflected  by  a  current  flowing 
in  a  wire  coiled  around  one  of  the 
needles ;  for,  as  shown  in  Fig.  82, 
the  current  which  flows  above  one 
needle  and  below  the  other  will  urge 
both  in  the  same  direction,  because 
they  are  already  in  reversed  positions. 
It  is  even  possible  to  go  farther,  and 
to  carry  the  wire  round  both  needles, 
winding  the  coil  around  the  upper  in 

the  opposite  sense  to  that  in  which  the  coil  is  wound 

round  the  lower  needle. 

Nobili  applied  the  astatic  arrangement  of  needles  to 

the  multiplying  coils  of  Schweigger,  and  thus  constructed 

a  very  sensitive  instrument,  the  Astatic  Galvanometer, 
Shown  in.  Fig.  88.     The  special  forms  of  galvanometer 

adapted  for  the  measurement  of  currents  are  described 

in  the  next  Lesson. 


Fig.  82. 


156  ELEMENTARY  LESSONS  ON       [CHAP,  in 

191.  Magnetic  field  due  to  Current.  —  Arago 
found  that  if  a  current  be  passed  through  a  piece  of  copper 
wire  it  becomes  capable  of  attracting  iron  filings  to  it 
so  long  as  the  current  flows.  These  filings  set  them- 
selves at  right  angles  to  the  wire,  and  cling  around  it, 
but  drop  off"  when  the  circuit  is  broken.  There  is,  then, 
a  magnetic  "  field,"  around  the  wire  which  carries  the 
current  ;  and  it  is  important  to  know  how  the  lines  cf 
force  are  distributed  in  this  field. 

Let  the  central  spot  in  Fig.  83  represent  an  imaginary 
cross-section  of  the  wire,  and  let  us  suppose  the  current 
to  be  flowing  in  through  the  paper  at  that  point.  Then 
by  Ampere's  rale  a  magnet  needle  placed  below  will.tend 
to  set  itself  in  the  position  shown,  with  its  N.  pole 
pointing  to  the  left.1  The  current  will  urge  a  needle 
above  the  wire  into  the  reverse  position.  A  needle  on 
the  right  of  the  current  will  set  itself  at  right  angles  to 
the  current  (i.e.  in  the  plane  of  the  paper),  and  with  its 

N.  pole  pointing  doivr^ 
while  the  N.  pole  of  a 
^  ,  .  needle  on  the  left  would 

\    Hi      /  V    fut          be  urSed  UP-    In  fact  the 

^ y  X^,   f     tendency  would  be  to  urge 

the  .N.    pole    round   the 
conductor    in    the    same 

way  as  the  nands  of  a  watch  move  ;  while  the  S.  pole 
would  be  urged  in  the  opposite  cyclic  direction  to  that  of 
the  hands  of  a  watch.  If  the  current  is  reversed,  and  is 
regarded  as  flowing  towards  the-  reader,  i.e.  coming  up 
out  of  the  plane  of  the  paper,  as  in  the  diagram  of  Fig. 

1  If  the  student  has  any  difficulty  in  applying  Ampere's  rule  to  this  case  and 
the  others  which  succeed,  he  should  carefully  follow  out  the  folfowing  mental 
operation.  Consider  the  spot  marked  "  in  "  as  a  hole  in  the  ground  into 
which  the  current  is  flowing,  and  into  which  he  dives  head-foremost.  While 
in  the  hole  he  must  turn  round  so  as  to  face  each  of  the  magnets  in  succession, 
and  remember  that  in  each  case  the  N. -seeking  pole  will  be  urged  to  his  left. 
In  diagram  84  he  must  conceive  himself  as  coming  up  out  of  the  hole  in  thr 
ground  where  the  current  is  flowing  out. 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM. 


157 


84,  then  the  motions  would  be  just  in  the  reverse  sense. 
It  Would  seem  from  this  as  if  a  N.- seeking  pole  of  a 
magnet  ought  to  revolve  continuously  round  and  round  a 
current ;  but  as  we  cannot  obtain  a  magnet  with  one 
pole  only,  and  as  the  S. -seeking  pole  is  urged  in  an 
opposite  direction,  all  that  occurs  is  that  the  needle  sets 
itself  as  a  tangent  to  a  circular  curve  surrounding  the 
conductor.  This  is  what  Oerstedt  meant  when  he 
described  the  electric  current  as  acting  "  in  a  revolving 
manner,"  upon  the  magnetic  needle.  The  field  of  force 
with  its  circular  lines  surrounding 
a  current  flowing  in  a  straight 
conductor,  can  be  examined  ex- 
perimentally with  iron  filings  in 
the  following  way :  A  card  is 
placed  horizontally  and  a  stout 
copper  wire  is  passed  vertically 
through  a  hole  in  it  (Fig.  85). 
Iron  filings  are  sifted  over  the 
card  (as  described  in  Art.  108), 
and  a  strong  current  from  three 
or  four  large  cells  is  passed  through  the  wire.  On 
tapping  the  card  gently  the  filings  near  the  wire  set 
themselves  in  concentric  circles  round  it. 

192.  Equivalent  Magnetic  Shell:  Ampere's 
Theorem. — For  many  purposes  the  following  way  of 
regarding  the  magnetic  action  of  electric  currents  is 
more  convenient  than  the  preceding.  Suppose  we  take 
a  battery  and  connect  its  terminals  by  a  circuit  of  wire, 
and  that  a  portion  of  the  circuit  be  twisted,  as  in  Fig.  86, 
into  a  looped  curve,  it  will  be  found  that  the  entire 
space  enclosed  by  the  loop  possesses  magnetic  properties. 
In  our  figure  the  current  is  supposed  to  be  flowing  round 
the  loop,  as  viewed  from  above,  in  the  same  direction  as 
the  hands  of  a  clock  move  round ;  an  imaginary  man 
swimming  round  the  circuit  and  always  facing  towards 
the  centre  would  have  his  left  side  down.  By  Ampere's 


Fig.  85. 


I5&'  ELEMENTARY  LESSONS  ON      [CHAP.  i;i. 

rule,  then,  a  N.  pole  would  be  urged  downwards  through 
the  loop,  while  a  S.  pole  would  be  urged  upwards.  In 
fact  the  space  enclosed  by  the  loop  of  the  circuit  behaves 


Fig.  86. 


like  a  magnetic  shell  (see" Art.  107),  having  its  upper  face 
of  S.-seekirig  magnetism,  and  its  lower  face  of  N. -seeking 
magnetism.  It  can  be  shown  in  every  case  that  a  closed 
voltaic  circuit  is  equivalent  to  a  magnetic  shell  whose 
edges  coincide  in  position  with  the  circiiit,  the  shell  being 
of  such  a  strength  that  the  number  of  its.  lines  of  force  is 
the  same  as  that  of  the  lines  of  force  due  to  the  current 
in  the  circuit.  The  circuit  acts  on  a  magnet  attracting 
or  repelling  it,  and  being  attracted  or  repelled  by  it,  just 
exactly  as  its  equivalent  magnetic  shell  would  do.  Also, 
the  circuit  itself,  when  placed  in  a  magnetic  field,  experi- 
ences the.  same  force  as  its  equivalent  magnetic  shell 
L would  do. 

193.  Maxwell's  Rule. —  Professor  Clerk  Maxwell, 
who  developed  this;  method  of  treating  the  subject,  has 
given  the  following  elegant  rule  for  determining  the 
mutual  action  of  a  circuit  and  a  magnet  placed  near  it. 
Every  portion  of  the  circuit  is  acted  upon  by  a  force 
'urging  it  in  such  a  direction  as  to  make  it  enctose 
geithin^its  embraceM^^reatest^ossible_number_o/  lines  of 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM.  159 

jorce.  If  the  circuit  is  fixed  and  the  magnet  movable, 
then  the  force  acting  on  the  magnet  will  also  be  such  as  to 
ter.d  to  make  the  number  of  lines  of  force  that  pass 
through  the  circuit  a  maximum  (see  also  Art.  3J7)- 

194.  De  la  Rive's  Floating  Battery. — The  pre- 
ceding remarks  may  be  illustrated  experimentally  by 
the  aid  of  a  little  floating  battery.  A  plate  of  zinc  and  one 
of  copper  (see  Fig.  87)  are  fixed  side  by  side  in  a  large 


cork,  and  connected  above  byaTcoil  of  covered  copper  wire 
bent  into  a  ring/^This  is  floated  upon  a  dish  containing 
dilute  sulphuric  acid.  If  one  pole  of  a  bar  magnet  be 
held  towards  the  ring  it  will  be  attracted  or  repelled 
according  to  the  pole  employed.  The  floating  circuit- 
will  behave  like  the  floating  magnet  in  Fig.  44,  except 
that  here  we  have  what  is  equivalent  to  a  floating 
magnetic  shell.  If  the  S.  pole  of  the  magnet  be  pre- 
sented to  that  face  of  the  ring  which  acts  as  a  S. -seeking 
pole  (viz.  that  face  round  which  the  current  is  flowing 


160  ELEMENTARY  LESSONS  ON       [CHAP.  MI 

in  a  clockwise  direction),  it  will  repel  it.  If  the  pole  b< 
thrust  right  into  the  ring,  and  then  held  still,  the  battery 
will  be  strongly  repelled,  will  draw  itself  off,  float  awsy, 
turn  round  so  as  to  present  toward  the  S.  pole  of  the 
magnet  its  N.-seeking  face,  will  th.en  be  attracted  ap, 
and  will  thread  itself  on  to  the  magnet  up  to  the  middle, 
in  which  position  as  many  magnetic  lines  of  force  as 
possible  cross  the  area  of  the  ring. 

It  can  be  shown  also  that  two  circuits  traversed  by 
currents  attract  and  repel  one  another  just  as  two 
magnetic  shells  would  do. 

It  will  be  explained  in  Lesson  XXVI.  on  Electro- 
magnets how  a  piece  of  iron/or  steel  can  be  magnetised 
by  causing  a  current  to  flow  in  a  spiral  wire  round  it. 

195.  Strength    of    the    Current    in   Magnetic 
Measure. — When  a  current  thus  acts  on  a  magnet  pole 
near  it,  the  force /which  it  exerts  will  be  proportional 
to  the  strength  /  of  the  current,  and  proportional  also 
to  the  strength  m  of  the  magnet  pole,  and  to  the  length 
/  of  the  wire  employed  :   it  will  also  vary  inversely  as 
the  square  of  the  distance  r  from   the  circuit   to  the 

i  I  tn 

magnet  pole.  Or,  /=  -^  dynes.  Suppose  the  wire 
looped  up  into  a  circle  round  the  magnet  pole,  then 
/  =  2irrt  and  /  =  — *  m  dynes.  Suppose  also  that  the 

circle  is  of  one  centimetre  radius,  and  that  the  magnet 
pole  is  of  strength  of  one  unit  (see  Art.  125),  then  the 

force  exerted  by  the  current  of  strength  /  will  be  2—  x  i , 

or  2iri  dynes.  In  order,  therefore,  that  a  current  oi 
strength  t  should  exert  a  force  of  /  dynes  on  the  unit  pole, 

one  must  consider  the  current  as  travelling  round  only  — 

271. 

part  of  the  circle,  or  round  a  portion  of  the  circum 
ference  equal  in  length  to  the  radius. 

196.  Unit   of  Current  Strength. — A  current   is 
said  to  have  a  strength  of  one  "  absolute  "  unit  when  ii 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM.  161 

is  such  that  if  one  centimetre  length  of  the  circuit  is  bent 
into  an  arc  of  one  centimetre  radius,  the  current  in  it 
exerts  a  force  of  one  dyne  on  a  magnet-pole  of  unit 
strength  placed  at  the  centre  of  the  arc.  The  practical 
unit  of  "  one  amplrs  ""  is  only  i\  of  this  theoretical  unit. 
also  Art.  323.) 


LESSON  XV  1  1  .  —  Galvanometers. 

197.  The  term  G-alvanometer  is  applied  to  an 
instrument  for  measuring  the  strength  of  electric 
currents  by  means  of  the  deflection  of  a  magnetic  needle, 
round  which  the  current  is  caused  to  flow  through  a  coil 
of  wire.  The  simple  arrangement  described  in  Art.  188 
was  termed  a  •'  Galvanoscope,"  or  current  indicator^  but 
it  could  not  .  rightly  be  termed  a  "galvanometer"1  or 
current  measurer,  because  its  indications  were  only 
qualitative,  not  quantitative.  The  indications  of  the 
needle  did  not  afford  accurate  knowledge  as  to  the  exact 
strength  of  current  flowing  through  the  instrument.  A 
good  galvanometer  must  fulfil  the  essential  condition  that 
its  readings  shall  really  measure  the  strength  of  the 
current  in  some  certain  way.  It  should  also  be  suffici- 
ently sensitive  for  the  currents  that  are  to  be  measured 
to  affect  it.  The  galvanometer  adapted  for  measuring 
very  small  currents  (say  a  current  of  only  one  or  tv/o 
millionth  parts  of  an  ampere)  will  not  be  suitable  for 
measuring  very  strong  currents,  such  as  are  used  in  pro- 
ducing an  electric  light.  Moreover,  if  the  current  to  be 
measured  has  already  passed  through  a  circuit  of  great 
resistance  (as,  for  example,  some  miles  of  telegraph 
wire),  a  galvanometer  whose  coil  is  a  short  one,  consist- 


1  The  terms  "  Rkfosco^f"  and  "  Rheomettr"  are  still  occasionally  applied 
to  these  instruments.  A  current  interrupter  is  sometimes  called  a  "  Rhea- 
tow,"  and  the  Commutator  or  Current  Reverser,  shown  in  Fig.  149,  is 
lu  some  books  called  a  "  Rhrotrop*  ;  but  the>e  terms  are  dropping  out  pf  -j.se. 

M 


1 62 


ELEMENTARY  LESSONS  ON      [CHAP,  in.1 


ing  only  of  a  few  turns  of  wire,  will  be  of  no  use,  and  a 
long-coil  galvanometer  must  be  employed  with  many 
turns  of  wire  round  the  needle.  The  reason  of  this  is, 
explained  hereafter  (Art.  352).  Hence  it  will  be  seen 
that  different  styles  of  instrument  are  needed  for  different 
kinds  of  work  ;  but  of  all  the  requisites  are  that  they 
should  afford  quantitative  measurements,  and. that  they 
should  be  sufficiently  sensitive  for  the  current  that  is  to 
be  measured. 

198.  Nobili's  Astatic  Galvanometer.  —  The 
instrument  constructed  by  Nobili,  consisting  of  an  astatic 
pair  of  needles  delicately  hung,  50  that  the  lower  one  lay 

within  a  coil  of  wire 
wound  upon  an  ivory 
frame  (Fig.  88),  was 
for  long  the  favourite 
form  of  sensitive 
galvanometer.  The 
needles  of  this  instru- 
ment, being  indepen- 
dent of  the  earth's 
magnetism,  take  their 
position  in  obedience 
to  the  torsion  of  the 
fibre  by  which  they 
are  hung.  The  frame 
on  which  the  coil  is 
wound  must  be  set 
carefully  parallel  to 


Fig.  88. 


the  needles ;  and  three  screw  feet  serve  to  adjust  the 
base  of  the  instrument  level.  Protection  against  cur- 
rents of  air  is  afforded  by  a  glass  shade.  When  a 
current  is  sent  through  the  wire  coils  the  needles  move 
to  right  or  left  over  a  graduated  circle.  When  the 
deflections  are  small  (i.e.  less  than  10°  or  j  5°),  they  are 
very  nearly  proportional  to  the  strength  of  the  currents 
that  produce  them.  Thus,  if  a  current  produces  a 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  163 

deflection  of  6°  it  is  known  to  be  approximately  three 
times  as  strong  as  a  current  which  only  turns  the  needle 
through  2°.  But  this  approximate  proportion  ceases  to 
be  true  if  the  deflection  is  more  than  15°  or  20°;  for 
then  the  needle  is  not  acted  upon  so  advantageously  by 
the  current,  since  the  poles  are  no  longer  within  the  coils, 
but  are  protruding  at  the  side,  and,  moreover,  the  needle 
being  oblique  to  the  force  acting  on  it,  part  only  of  the 
force  is  turning  it  against  the  directive  force  of  the  fibre ; 
the  other  part  of  the  force  is  uselessly  pulling  or  pushing 
the  needle  along  its  length.  It  is,  however,  possible  to 
"  calibrate  "  the  galvanometer, — that  is,  to  ascertain  by 
special  measurements,  or  by  comparison  with  a  standard 
instrument,  to  what  strengths  of  current  particular 
amounts  of  deflection  correspond.  Thus,  suppose  it  once 
known  that  a  deflection  of  32°  on  a  particular  galvano- 
meter is  produced  by  a  current  of  T^TS  of  an  ampere,  then 
a  current  of  that  strength  will  always  produce  on  that 
instrument  the  same  deflection,  unless  from  any  accident 
the  torsion  force  or  the  intensity  of  the  magnetic  field  is 
altered. 

199.  The  Tangent  Galvanometer. — It  is  not— 
for  the  reasons  mentioned  above — possible  to  construct 
a  galvanometer  in  which  the  angle  (as  measured  in 
degrees  of  arc)  through  which  the  needle  is  deflected  is 
proportional  throughout  its  whole  range  to  the  strength 
of  the  current.  But  it  is  possible  to  construct  a  very 
simple  galvanometer  in  which  the  tangent  *  of  the  angle 
of  deflection  shall  be  accurately  proportional  to  the 
strength  of  the  current.  Fig.  89  shows  a  frequent  form 
of  Tangent  G-alvanometer.  The  coil  of  this  instru- 
ment consists  of  a  simple  circle  of  stout  copper  wire 
from  ten  to  fifteen  inches  in  diameter.  At  the  centre  is 
delicately  suspended  a  magnetised  steel  needle  not- 
exceeding  one  inch  in  length,  and  usually  furnished  with 
a  light  index  of  aluminium.  The  instrument  is  adjusted 

'  See  note  on  Ways  jf  Reckoning  Angles,  p.  109. 


164 


ELEMENTARY  LESSONS  ON      [CHAP.  in. 


by  setting  the  coil  in  the  magnetic  meridian,  the  small 
needle  lying  then  in  the  plane  of  the  coil.  One  essential 
feature  of  this  arrangement  is,  that  while  the  coil  is  very 
large,  the  needle  is  relatively  very  small  The  "  field  " 


Fig.  89. 

due  to  a  current  passing  round  the  circle  is  very  uniform 
at  and  near  the  centre,  and  the  lines  of  force  are  there 
truly  normal  to  the  plane  of  the  coil.1  This  is  not  true 
of  other  parts  of  the  space  inside  the  ring,  the  force 
being  neither  uniform  nor  normal  in  directron,  except  in 
the  plane  of  the  coil  and  at  its  centre.  The  needle  being 

l  In  order  to  ensure  uniformity  of  field,  Gaugain  proposed  to  hang  the 
needle  at  a  point  on  the  axis  of  the  coil  distant  from  its  centre  by  a  distance 
equal  to  half  th.3  radius  of  the  coils.  Helmholtz  s  arrangement  of  two 
parallel  coils,  symmetrically  set  on  either  side  of  the  needle,  is  better  ;  and  a 
three-coil  galvanometer  having  the  central  coil  larger  than  the  others,  so  that 
all  three  may  lie  in  the  surface  of  a  sphere  having  the  small  needle  at  its 
centre,  is  the  best  arrangement  of  all  for  ensuring  that  the  field  at  th«  centre 
is  uniform. 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM.  165 

small  its  poles  are  never  far  from  the  centre,  and  hence 
n'ever  protrude  into  the  regions  where  the  magnetic  force 
is  irregular.  Whatever  magnetic  force  the  current  in 
the  coil  can  exert  on  the  needle  is  exerted  normally  to 
the  plane  of  the  ring,  and  therefore  at  right  angles  to 
the  magnetic  meridian.  Now,  it  was  proved  in  An.  124 
that  the  magnetic  force  which,  acting  at  right  angles  to 
the  meridian,  produces  on  a  magnetic  needle  the  de- 
flection 5  is  equal  to  the  horizontal  force  of  the  earth's 
magnetism  at  that  place  multiplied  by  the  tangent  of  the 
angle  of  deflection.  Bence  a  current  flowing  in  the  coil 
will  turn  the  needle  aside  through  an  angle  such  that  the 
tangent  of  the  angle  of  deflection  is  proportional  to  the 
strength  of  the  current. 

V- 

EXAMPLE. — Suppose  a  certain  battery  gave  a  deflection  of 
15°  on  a  tangent  galvanometer,  and  another  battery 
yielding  a  stronger  current  gave  a  deflection  of  30°.  The 
strengths  currents  are  Hot  in  the  proportion  of  15  : 30, 
but  in  the  proportion  of  tan  1 5°  to  tan  30°.  These 
values  must  be  obtained  from  a  Table  of  natural  tangents 
like  that  given  on  p.  in,  from  which  it  will  be  seen 
that  the  ratio  between  the  strengths  of  the  currents  is 
.  -268  :  -577,  or  about  10  :  22. 

Or,  more  generally,  if  current  C  produces  deflection  5,  and 
'  .current  C'  deflection  5',  then 

C  :C'  =  tan  6  :  tan  ? 

To  obviate  reference  to  a  table  of  figures,  the  circular 
scale  of  the  instrument  is  sometimes  graduated  into 
tangent  values  instead  of  being  divided  into  equal 
degrees  of  arc.  Let  a  tangent  O  T  be  drawn  to  the 
circle,  as  in  Fig.  90,  and  along  this  line  let  any  number 
of  equal  divisions  be  set  off,  beginning  at  O.  From 
these  points  draw  back  to  the  centre.  The  circle  .will 
thus  be  divided  into  a  number  of  pieces,  of  which  those 
near  O  are  nearly  equal,  but  which  get  smaller  and 
smaller  away  from  O.  These  unequal  pieces  correspond 


166 


ELEMENTARY  LESSONS  ON      [CHAP.  in. 


to  equal  increments  of  the  tangent.  If  the  scale  were 
divided  thus,  the  readings  would  be  proportional  to 
the  tangents.  It  is,  however,  harder  to  divide  an  arc 


Fig.  90. 

into  tangent-lines  with  accuracy  than  to  divide  it  into 
equal  degrees  ;  hence  this  graduation,  though  convenient, 
is  not  used  where  great  accuracy  is  needed. 

200.  Absolute  Measure  of  Current  by  Tangent  Gal- 
vanometer.— The  strength  of  a  current  may  be  determined  in 
"  absolute  "  units  by  the  aid  of  the  tangent  galvanometer  if  the 
"  constants  "  of  the  instrument  are  known.  The  tangent  of  the 
angle  of  deflection  represents  (see  Art.  124)  the  ratio  between 
the  magnetic  force  due  to  the  current  and  the  horizontal  com- 
ponent of  the  earth's  magnetic  force.  Both  these  forces  act  on 
the  needle,  and  depend  equally  upon  the  magnetic  moment  of  the 
needle,  which,  therefore,  we  need  not  know  for  this  purpose. 
We  know  that  the  force  exerted  by  the  current  at  centre  of  the 
coil  is  proportional  to  the  horizontal  force  of  the  earth's  mag 
netism  multiplied  by  the  tangent  of  the  angle  of  deflection. 
These  two  quantities  can  be  found  from  the  tables,  and  from 
them  we  calculate  the  absolute  value  of  the  current,  as  follows  : — 
Let  r  represent  the  radius  of  the  galvanometer  coil  (measured  in 
centimetres) ;  its  total  length  (if  of  one  turn  only)  is  2vr.  The 
distance  from  the  centre  to  all  parts  of  the  coil  is  of  course  r. 
From  our  definition  of  the  unit  of  strength  of  current  (Art.  196), 

it  follows  that        i  x   ~^-  —  force  (in  dynes)  at  centre, 


or 


t  x  -       =  H  '  tan  S  ; 


hence      i     =      —  •  H  *  tan  3. 


CHAP.  Hi.]  ELECTRICITY  AND  MAGNETISM.  167 


y 

The  quantity        is  called  the  "  constant  "  of  the  galvanometer. 

Hence  we  obtain  the  value  of  the  current  in  absolute  (electro- 
magnetic) units  1  by  multiplying  together  the  galvanometer  con- 
stant, the  horizontal  magnetic  force  at  the  place,  and  the  tangent 
of  the  angle  of  deflection.  Tangent  galvanometers  aie  often 
made  with  more  than  one  turn  of  wire.  In  this  case  the  "  con- 

m 

slant  "  is  -  where  n  is  the  number  of  turns  in  the  coil. 


200  (£/*).  Am-meter.  —  Professors  Ayrton  and  Perry  have  lately  design«J 
Bome  galvanometers  for  electric-light  work,  intended  to  show  by  a  pointer 
attached  to  the  magnetic  needle  the  strength  of  the  current  in  aniph  es  {Art. 
323).  In  these  instruments,  which  are  portable,  and  "dead-beat  '  in  action. 
the  needle  is  placed  between  the  poles  of  a  powerful  permanent  magnet  to 
control  its  direction  and  make  it  independent  of  the  earth's  magnetism.  By 
a  peculiar  shaping  of  the  pole-pieces,  needle,  and  coils,  the  angular  deflections 
are  proportional  to  the  strength  of  the  deflecting  current  The  coils  are  in 
ten  sections,  which  can  be  grouped  either  "  in  series  "  or  "  in  parallel  *  at 
will,  by  turning  an  appropriate  commutator,  thus  enabling  the  scale-readings 
to  be  verified  by  using  one  ordinary  celL  These  A  m-mttert  are  made  with 
short-coils  of  very  low  resistance  and  few  turns  of  wire.  Ayrton  and  Perry 
have  also  arranged  Voltmeters  (see  Art.  360  d\  with  long-coils  of  high  re- 
sistance, in  a  similar  way. 

2O1.  Sine  Galvanometer.  —  The  disadvantage  of 
the  tangent  galvanometer  just  described  is  that  it  is  not 
very  sensitive,  because  the  coil  is  necessarily  very  large 
us  compared  with  the  needle,  and  therefore  far  a\\ay 
from  it.  A  galvanometer  with  a  smaller  coil  or  a  larger 
needle  could  not  be  used  as  a  tangent  galvanometer, 
though  it  would  be  more  sensitive.  Any  sensitive 
galvanometer  in  which  the  needle  is  directed  by  the 
earth's  magnetism  can,  however,  be  used  as  a  Sine 
Galvanometer,  provided  the  frame  on  which  the  coils 
are  wound  is  capable  of  being  turned  round  a  central 
axis.  When  the  instrument  is  so  constructed,  the 
following  method  of  measuring  currents  is  adopted. 
The  coils  are  first  set  parallel  to  the  needle  (i.e.  in  the 
magnetic  meridian)  ;  the  current  is  then  sent  through 
it,  producing  a  deflection  ;  the  coil  itself  is  rotated  round 
in  the  same  sense,  and,  if  turned  round  througn  a  wide 

1  The  Kudent  will  learn  (Art.  196  and  323)  that  the  practical  unit  of 
current  which  we  call  "  one  atnfirt"  is  only  *o  of  one  "  absolute  "  unit  of  tae 
centimetre  -gramme-second  system. 


i68  ELEMENTARY  LESSONS  ON       [CHAP,  in; 

enough'angle,  will  overtake  the  needle,'  which'  will  once 
more  lie  parallel  to  the  coil.  In  this  position  two  forces 
are  acting  on  the  needle  :  the  directive  force  of  the 
earth's  magnetism  acting  along  the  magnetic  meridian, 
and  the  force  due  to  the  current  passing  in  the  coil, 
which  tends  to  thrust  the  poles  of  the  needle  out  at 
right  angles  ;  in  Tact  there  is  a  "couple"  which  exactly 
balances  the  "  couple "  due  to  terrestrial  magnetism. 
Now  it  was  shown  in  the  Lesson  on  the  Laws  of  Mag- 
netic Force  (Art.  123),  that  when  a  needle  is  deflected 
the  "  moment "  of  the  couple  is  proportional  to  the  sine 
of  the  angle  of  deflection.  Hence  in  the  sine  galvano- 
meter, when  the  coil  has  been  turned  round  so  that  the 
needle  once  more  lies  along  it,  the  strength  of  the  current 
in  the  coil  is  proportional  to  the  sine  of  the  angle  through 
which  the  coil  has  been  turned. J 

2O2.  The  Mirror  Galvanometer. —When  a  gal- 
vanometer of  great  delicacy  is  needed,  the  moving  parts 
must  be  made  very  light  and  small.  To  watch  the 
movements  of  a  very  small  needle  an  index  of  some 
kind  must  be  used  ;  indeed,  in  the  tangent  galvanometer 
it  is  usual  to  fasten  to  the  short  stout  needle  a  delicate 
stiff  pointer  of  aluminium.  A  far  better  method  is  to 
fasten  to  the  needle  a  veiy  light  mirror  of  silvered  glass, 
by  means  of  which  a  beam  of  light  can  be  reflected  on 
to  a  scale,  so  that  every  slightest  motion  of  the  needle 
is  magnified  and  made  apparent.  The  mirror  galvano- 

•  !  Again  the  student  who  desires  to  compare  the  'strength  of  two  currents 
will  require  the  help  of  a  Table  of  natural  sines,  like  that  given  on  page  in. 
Suppose  that  with  current  C  the  coils  had  to  be  turned  through  an  angle  of 
(9  degrees ;  and  that  with  a  different  current  C'  the  coils  had  to  be  turned 
through  ff  degrees,  then 

C  :  C  —  sin  0  '•  sin  ff. 

It  is  of  course  assumed  that  -the  instrument  is  provided  with  a  scale  of 
degrees  on  which  to  read  off  the  angle  through  which  the  coils  have  been 
turned.  It  is  possible  here  also,  for  rough  purposes,  to  graduate  the  circle 
not  in  degrees  of  arc  but  in  portions  corresponding  to  equal  additional 
values  of  the  sine.  The  student  should  try  this  way  of  dividing  a  circle 
after /eading  the  note  On  Ways  o£  Reckoning  A  nglesj 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM. 


169 


meters  devised  by  Sir.  W.  Thomson  for  signalling  through 
submarine  cables,  are  admirable  examples  of  this  class 
of  instrument.  In  Fig.  91  the  general  arrangements  of 
this  instrument  are  shown.  The  body  of  the  galvano- 
meter is  supported  on  three  screw  feet  by  which  it  can 
be  adjusted.  The  magnet  consists  of  one  or  more 
small  pieces  of  steel  watch-spring  attached  to  the  back 


Fig.  91 

of  a  light  concave  silvered  glass  mirror  about  as  large 
as  a  threepenny  piece.  This  mirror  is  hung  by  a  single 
fibre  of  cocoon  silk  within  the  coil,  and  a  curved  magnet, 
which  selves  to  counteract  the  magnetism  of  the  earth, 
or  to  direct  the  needle,  is  carried  upon  a  vertical  support 
above.  Opposite  the  galvanometer  is  placed  the  scale. 
A  beam  of  light  from  a  paraffin  lamp  passes  through 
a  narrojv  aperture  under  the  scale  and  falls  on  the 
mirror,  vVhich  reflects  it  back  on  to  the  scale.  The 
mirror  is  slightly  concave,  and  gives  a  well  defined  spot 
of  light  if  the  scale  is  adjusted  to  suit  the  focus  of  the 


170  ELEMENTARY  LESSONS  ON       [CHAP.  III. 

mirror.1  The  adjusting  magnet  enables  the  operator  to 
bring  the  reflected  spot  of  light  to  the  zero  point  at  the 
middle  of  the  scale.  The  feeblest  current  passing  through 
the  galvanometer  will  cause  the  spot  of  light  to  shift  to 
right  or  left.  The  tiny  current  generated  by  dipping 
into  a  drop  of  salt  water  the  tip  of  a  brass  pin  and  a 
steel  needle  (connected  by  wires  to  the  terminals  of  the 
galvanometer)  will  send  the  spot  of  light  swinging  right 
across- the  scale.  If  a  powerful  lime-light  is  used,  the 
movement  of  the  needle  can  be  shown  to  a  thousand 
persons  at  once.  For  still  more  delicate  work  an  astatic 
pair  of  needles  can  be  used,  each  being  surrounded  by 
its  coil,  and  having  the  mirror  rigidly  attached  to  one  of 
the  needles. 

Strong  currents  must  not  be  passed  through  very 
sensitive  galvanometers,  for,  even  if  they  are  not  spoiled, 
the  deflections  of  the  needle  will  be  too  lirge  to  give 
accurate  measurements.  In  such  cases  the  galvan- 
ometer is  used  with  a  s/iunf,  or  coil  of  wire  arranged  so 
that  the  greater  part  of  the  current  shall  flow  through  it, 
and  pass  the  galvanometer  by,  only  a  small  portion  of  the 
current  actually  traversing  the  coils  of  the  instrument. 
The  resistance  of  the  shunt  must  bear  a  known  ratio  to 
the  resistance  of  the  instrument,  according  to  the  prin 
ciple  laid  down  in  Art.  353  about  branched  circuits. 

2O3.  Differential  Galvanometer. —  For  the  pur- 
pose  of  comparing  two  currents  a  galvanometer  is 
sometimes  employed,  in  which  the  coil  consists  of  two 
separate  wires  wound  side  by  side.  If  two  equal  currents 
are  sent  in  opposite  directions  through  these  wires,  the 
needle  will  not  move.  If  the  currents  are,  however, 
unequal,  then  the  needle  will  be  moved  by  the  stronger 

1  As  concave  mirrors  are  expensive,  a  plain  mirror  "behind  a  lens  of 
suitable  focus  may  be  substituted.  The  thin  discs  of  glass  used  in 
mounting  objects  for  the  microscope  form,  when  silvered,  excellent  light 
mirrors.  Where  great  accuracy  is  desired  a  fine  wire  is  placed  in  the 
aperture  traversed  by  the  beam  of  light,  and  the  image  of  this  appear* 
when  focused  on  the  screen  as  a  dark  line  crossing  the  spot  of  light. 


CHAP,  in.)   ELECTRICITY  AND  MAGNETISM.  171 

of  them,  with  an  intensity  corresponding  to  the  difference 
of  the  strengths  of  the  two  currents 

204.  Ballistic  Galvanometer. — In  order  to  measure 
the  strength  of  currents  which  last  only  a  very  short  time, 
galvanometers  are  employed  in  which  the  needle  takes 
a  relatively  long  time  to  swing.     T^his  is  the  case  with 
long  or  heavy  needles ;  or  the  needles  may  be  weighted 
by  enclosing  them  in  leaden  cases.     As  the  needle  swir  ^s 
slowly  round,  it  adds  up,  as  it  were,  the  varying  impulses' 
received    during    the    passage    of   a    transient    current. 
Tlie  sine  of  half  the  angle  of  the  first  siving  is  proportional 
to  the  quantity  of  electricity  that  has  flowed  through  the 
coil.     The  charge  of  a  condenser  may  thus  be  measured 
by  discharging  it  through  a  ballistic  galvanometer. 

LESSON  XVIII. — Chemical  Actions  of  the  Citrrent : — 
Voltameters. 

205.  In  addition  to  the  chemical  actions  inside  the 
cells  of  the  battery,  which  always  accompany  the  produc- 
tion of  a  current,  there  are  also  chemical  actions  produced 
outside  the  battery  when   the   current   is  caused  to  pass 
through  certain  liquids.      Liquids  may  be  divided  into 
three  classes — (i)  those  which  do  not  conduct  at  all,  such 
as  turpentine  and  many  oils,  particularly  petroleum  ;  (2). 
those  which  conduct  without  decomposition,  viz.  mercury 
and  other  molten  metals,  which  conduct  just  as  solid 
metals  do  ;   (3)  those  which  are  decomposed  when  they 
conduct   a  current,  viz.    the    dilute    acids,    solutions    of 
metallic  salts,  and  certain  fused  solid  compounds. 

206.  Decomposition  of  Water. — In  the  year  1 800 
Carlisle  and  Nicholson  discovered  that  the  voltaic  current 
could  be  passed  through  water,  and  that  in  passing  through 
it  decomposed  a  portion  of  the  liquid  into  its  constituent 
gases.      These  gases  appeared  in  bubbles  on  the  ends  of 
the   wires   which    led   the  current   into   and   out   of  the 
liquid ;  bubbles  of  oxygen  gas   appearing  at   the   point 


172  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

where  the  current  entered  the  liquid,  and  hydrogen 
bubbles  where  it  left  the  liquid.  It  was  soon  found  that 
a  great  many  other  liquids,  particularly  dilute  acids  and 
solutions  of  metallic  salts,  could.be  similarly  decomposed 
by' passing  a  current  through  them. 

207.  Electrolysis. — To  this- process  of  decomposing 
a  liquid  by  means  of  an  electric  current  Faraday  gave 
the  name  of  electrolysis  (i.e.  electric  analysis) ;  and 
those  substances' which  are/capable  of  being  thus  decom- 
posed or  "  electrolysed  "  he  termed  electrolytes. 

The  ends  of  the  wires  leading  from  and  to  the  battery 
are  called  electrodes  ;  and  to  distinguish  them,  that  by 
which  the  current  enters  is  called  the  anode,  that  by 
which  it  leaves  the  kathode.  The  vessel  in  which  a 
liquid  is  placed  for  electrolysis  is  termed  an  electrolytic  cell. 

208.  Electrolysis  of  Water. — Returning  to   the 
decomposition  of  water,  we  may  remark  that  perfectly 
pure  water  appears  not  to  conduct,  but  its  resistance  is 
greatly  reduced  by  the  addition  of  a  few  drops  of  sul- 
phuric or  of  hydrochloric  acid.     The  apparatus  shown  in 
Fig.  92  is  suitable  for  this  purpose.     Here  a  battery  of 
two  cells  (those  shown  are  circular  Bunsen's  batteries) 
is  seen  with  its  poles  connected  to  two  strips  of  metallic 
platinum  as  electrodes,  which  project  up  into  a  vessel  con- 
taining the  acidulated  water.     Two  tubes  closed  at  one 
end,  which  have  been  previously  filled  with  water  and 
inverted,  receive  the  gases  evolved   at  the   electrodes. 

I  Platinum  is  preferred  to  other  metals  such  as  copper  or 
iron  for  electrodes,  since  it  is  less  oxidisable  and  .resists 
every  a.cid.  It  is  found  that  there  is  almost  exactly 
twice  as  much  hydrogen  gas  (by  volume)  evolved  at  the 
kathode  as  there  is  of  oxygen  at  the  anode.  This  fact 
corresponds  with  the  known  chemical  composition  of 
water,  which  is  produced  by  combining  together  these 
two  gases  in  the  proportion  of  two  volumes  of  the 
former  to  one  of  the  latter.  '  .The  proportions  of  gases 
evolyed,  however,  are  not  exactly  two  to  one,  for  at  first  a. 


CHAP.  HI.]  ELECTRICITY  AND  MAGNETISM. 


173 


very  small  quantity  of  the  hydrogen  is  absorbed  or 
"  occluded  "  by  the  platinum  surface,  while  a  more  con- 
siderable proportion  of,  the  oxygen — about  I  per  cent— 


Fig  92. 

is  given  off  in  the  denser  allotropic  form  of  osone,  which 
occupies  less  space  and  is  also  slightly  soluble  in  the 
water.  When  a  sufficient  amount  of  the  gases  has  been 
evolved  and  collected  they  may  be  tested  ;  the  hydrogen 
by  showing  that  it  will  Burn,  the  oxygen  by  its  causing 
a  glowing  spark  on  the  end  of  a  'splinter  of  wood  to  burst 
into  flame.  If  the  two  gases  are  collected  together  in  a 
common  receiver,  the  mixed  gas  will  be  found  to  possess 
the  well  known  explosive  property  of  mixed  hydrogen 
and  oxygen  gases.  The  chemical  decomposition  is  ex- 
pressed in  the  following  equation  : 

HaO          =  H,  +o 

Water  yields        ,  a  vols.  of  Hydrogen          £nd      i  vol.  of  Oxygen. 

2O9.  Electrolysis  of  Sulphate  of  Copper. — We 

will  take  as  another  case  the  electrolysis  of  a  solution  of 
the  well-known  ^i>lue  vitriol"  or  sulphate  of  copper^  If 


174  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

a  few  crystals  of  this  substance  are  dissolved  in  watoi 
a  blue  liquid  is  obtained,  which  is  easily  electrolysed 
between  two  electrodes  of  platinum  foil,  by  the  current 
from  a  single  cell  of  any  ordinary  battery.  The  chemical 
formula  for  sulphate  of  copper  is  CuSO,.  The  result  of 
the  electrolysis  is  to  split  it  up  into  metallic  copper, 
which  is  deposited  in  a  film  upon  the  kathode,  and 
"  Sulphion  "  an  easily  decomposed  compound  of  sulphcr 
and  oxygen,  which  is  immediately  acted  upon  by  the 
water  forming  sulphuric  acid  and  oxygen.  This  oxygen 
is  liberated  in  bubbles  at  the  anode.  The  chemical 
changes  are  thus  expressed  : 

CuSO4  =  Cu          +          SO4 

Sulphate  of  Copper          becomes          Copper         and          Sulphiou , 

SO4        +      H,O         =  H2SO4          +          O 

Sulphion       and       water        produce        Sulphuric  acid        and        Oxygen. 

In  this  uay,  as  the  current  continues  to  flow,  copper  is 
continually  withdrawn  from  the  liquid  and  deposited  on 
the  kathode,  and  the  liquid  gets  more  and  more  acid.  If 
copper  electrodes  are  used,  instead  of  platinum,  no  oxygen 
is  given  off  at  the  anode,  but  the  copper  anode  itself  dis- 
solves away  into  the  liquid  at  exactly  the  same  rate  as 
the  copper  of  the  liquid  is  deposited  on  the  kathode. 

21O.  Anions  and  Kathions. — The  atoms  \\hicb 
thus  are  severed  from  one  another  and  carried  imisibly 
by  the  current  to  the  electrodes,  and  there  deposited, 
are  obviously  of  two  classes  :  one  set  go  to  the  anode, 
the  other  to  the  kathode.  Faraday  gave  the  name  of 
ions  to  these  wandering  atoms  ;  those  going  to  the 
anode  being  anions,  and  those  going  to  the  kathode 
being  kathions.  Anions  are  sometimes  regarded  as 
"  electro-negative  "  because  they  move  as  if  attracted 
toward  the  -f  pole  of  the  battery,  while  the  kathions 
are  regarded  as  "  electro-positive."  Hydrogen  and  the 
metals  are  kathions,  moving  apparently  with  the  direction 
assumed  as  that  of  the  current,  and  are  deposited'  where 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  175 

the  current  leaves  the  electrolytic  cell.  The  anions  are 
oxygen,  chlorine,  etc.  When,  for  example,  chloride  oi 
tin  is  electrolysed,  metallic  tin  is  deposited  on  the  kath- 
ode, and  chlorine  gas  is  evolved  at  the  anode. 

211.  Quantitative  Laws  of  Electrolysis. 

(I.)  The  amount  oj  chemical  action  is  equal  at  all  prinli, 
of  a  circuit.  If  two  or  more  electrolytic  cells  are  placed 
at  different  points  of  a  circuit  the  amount  of  chemical 
action  will  be  the  same  in  all,  for  the  same  qu'antity  of 
electricity  flows  past  every  point  of  the  circuit  in  the 
same,  time.  If  all  these  cells  contain  acidulated  water, 
the  quantity,  for  example,  of  hydrogen  set  free  in  each 
will  be  the  same  ; .  or,  if  they  contain  a  solution  of 
sulphate  of  copper,  identical  quantities  of  copper  will  be 
deposited  in  each;  If  some  of  the  cells  contain  acidu- 
lated water,  and  others  contain 'sulphate  of  copper,  the 
weights  of  hydrogen  and  of  copper  "will,  not  be  equal., 
but  will  be  in  chemically  equivalent  quantities. 

(ii.)  The  amount  of  an  ion  liberated  at  an* electrode 
in  a  given  lime  ^  is  proportional  to  the  strength  of  the 
current.  A  current  of  2  amperes  will  cause  just  twice 
the  quantity  of  chemical  decomposition  to  take  place  as 
a  current  of  i  ampere  would  do  in  the  same  time. 

(iii.)  The  amount) of  an  ion  liberated  at  an  -electrode 
in  one  second  is  equal  to  the  strength  of  the  current 
multiplied  by  t  the  "  electro -chemical  equivalent"  of  the 
ion.  It  has  been  found  by  experiment  that  the  passage 
of  one  coulomb  of  electricity  through  water  liberates 
•000010352  gramme1  of  hydrogen.  -Hence,  a  current 
the  strength  of  which  "is  C  ^amperes)  will  liberate  C  x 
•000010352  grammes  of  hydrogen  per  second.  The 
quantity  -00001035?.  'ls  called  the  electro-chemical  equiva- 
Icnt  of  hydrogen.  The  ", electro-chemical  equivalents" 
of  other  elements  can  be  easily  calculated  if  their 
chemical  "equivalent"  is  known.  Thus -the  chemical 

l  Lord  Rayleigh  says  '000010352  ;  Mascart,  '000010415  ;  F.  and  W.  Kohl 
yausch,  '000010354. 


176 


ELEMENTARY  LESSONS  ON       [CHAP,  in, 


"equivalent"1  of  copper  is  31*5;  multiplying  this  by 
•000010352  we  get  as  the  electro-chemical  equivalent  of 
copper  the  value  -0003261  (gramme). 


212.  TABLE  OF  ELECTRO-CHEMICAL  EQUIVALENTS.  ETC. 


Atomic 
Weight. 

Val- 
ency 

Chemical 
Eouivalent 

Electro-chemical 
Equivalent 
(grammes 
per  coulomb). 

Electropositive  — 
Hydrogen  .... 
Potassium  .... 
Sodium       .... 

I' 

39'i 

21' 

I 
I 
I 

I 

39'i 

21' 

•000010352 
•0004047 
•0002381 

Gold     
Silver    ..... 

196  '6 
1  08' 

3 
i 

65-5 

1  08- 

•0006780 
-oo  iii  So 

Copper  (Cupric)  . 
',        (Cuprose) 
Mercury  (Mercuric)   . 
,,         (Mercurose) 
Tin  (Stannic)  .     .     . 
„     (Stannose)     . 
Iron  (Ferric)    .     . 
„     (Ferrose)       .     . 
Nickel  

63- 
63- 

200* 

20O  ' 

118- 
118- 
56' 
56- 

so* 

2 
I 
2 
I 

4 

2 

3 

2 
2 

31'S 
63- 
ioo- 

200' 
29-5 

59' 
18-6 
28- 

20'? 

•0003261 
•0006522 
•0010351 
•0020702 
•0003054 
•0006  1  oS 
0*0001932 
•0002898 

'OOQT.OS.A. 

zinc   r.   .   .   .   . 

Lead    \     .     .     .     . 
Electronegative  — 
Oxygen       .... 
Chlorine     .... 

65' 
207* 

16- 

35'5 

T  27  ' 

2 
2 

2 
I 
1 

32-5 

1  03  '5 

8- 

35'S 

127* 

•0003364 
•0010684 

•OO00828 
•0003675 
'OOI1I47 

Bromine     .... 
Nitrogen     .... 

SO' 
14* 

I 

3 

80- 

4'3 

•0008282 
•0000445 

1  The  chemical  "equivalent"  must  not  be  confounded  with  the  "atomic 
weight."  The  atomic  weight  of  copper  is  63,  that  is  to  say,  its  atoms  are  63 
times  as  heavy  as  atoms  of  hydrogen.  But  in  chemical  combinations  one 
atom  of  copper  replaces^  or  is  "worth,"  two  atoms  of  hydrogen  ;  hence  the 
weight  of  copper  equivalent  to  i  of  hydrogen  is  V  —  31  \.  In  all  cases  the  I 

,       .     ,  ,.        .     .                                          atomic  wei&!,c. 
chemical    'equivalent"  is  the  quotient  „,!,...,.;:- —     The  above 

gives  full  statistical  information. 


valency 


CHAP,  in.]  ELECTRICITY  AND  MAGNETISM.  177 

213.  The  following   equation   embodies   the   rule  for 
finding  the  weight  of  any  given  ion  disengaged  from  an 
electrolytic  solution  during  a  known  time  by  a  current 
whose  strength  is  known.      Let  C  be  the  strength  of  the 
current  (reckoned  in  amplres\  t  the  time  (in  seconds), 
z  the  electro-chemical  equivalent,  and  w  the  weight  (in 
grammes)  of  the  element  liberated  :  then 

iv  =  sCt, 

or,  in  words,  the  weight  (in  grammes)  of  an  element 
deposited  by  electrolysis  is  found  by  multiplying  its 
electro-chemical  equivalent  by  the  strength  of  the  current 
(reckoned  in  amperes),  and  by  the  time  (in  seconds), 
during  which  the  current  continues  to  flow. 

EXAMPLE.— -A  current  from  five  Daniell's  cells  was  passed 
through  two  electrolytic  cells,  one  containing  a  solution 
of  silver,  the  other  acidulated  water,  for  ten  minutes. 
A  tangent  galvanometer  in  the*  circuit  showed  the 
strength  of  the  current  to  be  '5  ampins.  The  weight 
of  silver  deposited  will  be  'OOinSo  x  -5  x  10  x  60 
=  "3354  gramme.  The  weight  of  hydrogen  evolved 
in  the  second  cell  will  be  '000010352  x  -5  x  10  x  60 
=  "0031056  gramme. 

214.  Voltameters. — The  second  of  the  above  laws, 
that  the  amount  of  an  ion  liberated  in  a  given  time  is 
proportional  to  the  strength  of  the  current,  is  sometimes 
known  as  Faraday's  Law^  from  its  discoverer.      Faraday 
pointed  out  that  it  affords  a  chemical  means  of  measur- 
ing the  strength   of  currents.      He  gave  the  name  of 
voltameter  to    an   electrolytic   cell    arranged  for   the 
purpose  of  measuring  the   strength   of  the   current  by 
the  amount  of  chemical  action  it  effects. 

215.  Water -Voltameter. — The   apparatus   shown 
in   Fi<j.   92   might    be    appropriately   termed  a  Water- 
Voltameter,   provided    the    tubes    to    collect    the   gases 
be  graduated,  so  as  to  measure  the  quantities  evolvedi 

N 


i;8  ELEMENTARY  LESSONS  ON      [CHAP,  ill 

The  weight  of  each  measured  cubic  centimetre  of  hydro 
gen  (at  the  standard  temperature  of  o°  C,  and  pressure 
of  760  millims.)-  is  known  *to  be  -0000896  grammes. 
Hence,  if  the  number  of  cubic  centimetres  liberated 
during  a  given  time  by  a  current  of  unknown  strength 
be  ascertained,  the  strength  of  the  current  can  be  calcu- 
lated by  first  reducing  the  volume  to  weight,  and  then 
dividing  by  the  electro-chemical  equivalent,  and  by  the 
time.  Each  coulomb  of  electricity  liberates  in  its  flow 
•1157  cubic  centimetres  of  hydrogen,  and  -0579  c  c. 
of  oxygen.  If  these  gases  are  collected  together  in  a 
mixed-gas  voltameter  there  will  be  -1736  c.  c.  of  the 
mixed  gases  evolved  for  every  coulomb  of  electricity 
which  passes.  To  decompose  9  grammes  of  water, 
liberating  i  gramme  of  H  and  8  grammes  of  O,  requires 
96,600  coulombs. 

216.  Copper    and    Silver  Voltameters.  —  As   mentioned 
above,  if  sulphate  of  copper  is  electrolysed  between  two  elec- 
trodes of  copper,  the  anode  is  slowly  dissolved,  and  the  kathode 
receives  an  equal  quantity  of  copper  as  a  deposit  on  its  surface.' 
One  coulomb  of  electricity  will  cause  '0003261   gramme  to  be 
deposited ;  and  to  deposit  one  gramme  weight  requires  a  total 
quantity  of  3066  coulombs  to  flow  through  the  electrodes.     A 
current  of  one  ampere  deposits  in  one  hour   I'i74  grammes  of 
copper,  or  4/025  grammes  of  silver. 

By  weighing  one  of  the  electrodes  before  and  after  the  passage  of  a  current, 
the  gain  (or  loss)  will  be  proportional  to  the  quantity  of  electricity  that  hr.s 
passed.  In  1879  Edison,  the  iventorj  proposed  to  apply  this  method  for 
measuring  the  quantity  of  electricity  supplied  to  houses  for  electric  lights  in 
them ;  a  small  copper  Voltameter  being  placed  in  a  branch  of  ihe  circuit 
which  supplied  the  house,  to  serve  as  a  meter.  Various  other  kinds  o' 
Coulomlmetert  have  been  proposed,  having  clockwork  counters,  rolling 
integrating  discs,  and  other  mechanical  devices  to  add  up  the  total  quantity 
of  electricity  conveyed  by  the  current 

217.  Comparison   of   Voltameters  -with    Gal- 
vanometers.— It  will  be  seen  that  both  Galvanometers 
and  Voltameters  are  intended  to  measure  the  strength  of 
currents,  one  by  magnetic,  the  other  by  chemical  means. 
Faraday  demonstrated  that  the  magnetic  and  the  chemical 
actions  of  a  current  are   proportional  to   one   another 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  179 

The  galvanometer  shows,  however,  the  strength  of  the 
current  at  any  moment,  and  its  variations  in  strength 
from  one  moment  to  another,  by  the  position  of  the 
needle.  In  the  Voltameter,  a  varying  current  may 
liberate  the  bubbles  of  gas  or  the  atoms  of  copper  rapidly 
at  one  moment,  and  slowly  the  next,  but  all  the  varying 
quantities  will  be  simply  added  together  in  the  total 
yield.  In  fact,  the  voltameter  gives  us  the  "  time 
integral "  of  the  current.  It  tells  us  what  quantity  of 
electricity  has  flowed  through  it  during  the  experiment, 
rather  than  how  strong  the  current  was  at  any  one 
moment. 

218.  Chemical  Test  for  "Weak  Currents.  —  A 
very  feeble  current  suffices  to  produce  a  perceptible 
amount  of  change  in  certain  chemical  substances.  If 
a  few  crystals  of  the  white  salt  iodide  of  potassium  are 
dissolved  in  water,  and  then  a  little  starch  paste  is  added, 
a  very  sensitive  electrolyte  is  obtained,  which  turns  to 
an  indigo  blue  colour  at  the  anode  when  a  very  weak 
current  passes  through  it.  The  decomposition  of  the 
salt  liberates  iodine  at  the  anode,  which,  acting  on  the 
starch,  forms  a  coloured  compound.  White  blotting- 
paper,  dipped  into  the  prepared  liquid,  and  then  laid  on 
the  kathode  and  touched  by  the  anode,  affords  a  con- 
venient way  of  examining  the  discoloration  due  to  a 
current.  A  solution  of  Ferrocyanide  of  Potassium  affords 
similarly  on  electrolysis  the  well-known  tint  of  Prussian 
Blue.  Bain  proposed  to  utilise  this  in  a  Chemical 
Writing  Telegraph,  the  short  and  long  currents  trans- 
mitted along  the  line  from  a  battery  being  thus  recorded 
in  blue  marks  on  a  strip  of  prepared  paper,  drawn  along 
by  clockwork  under  the  terminal  of  the  positive  wire. 
Faraday  showed  that  chemical  discoloration  of  paper 
moistened  with  starch  and  iodide  of  potassium  was  pro- 
duced by  the  passage  of  all  different  kinds  of  electricity — 
frictional,  voltaic,  thermo-electric,  and  magneto  -  electric, 
— even  by  that  evolved  by  the  Torpedo  and  tb« 


i8o  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

Gymnotus.     In  fact,  he  relied  on  this  chemical  test  as 
one  proof  of  the  identity  of  the  different  kinds. 

219.  Internal   and   External   Actions.  —  In   an 
earlier  Lesson  it  was  shown  that  the  quantity  of  chemical 
action  inside  the  cells  of  the  battery  was  proportional  to 
the  strength  of  the  current.     Hence,  Law  (i.)  of  Art.  211, 
applies   both   to   the  portion   of  the   circuit  within   the 
battery  and  to  that  without  it. 

Suppose  3  Daniell's  cells  are  being  employed  to  decompose 
water  in  a  voltameter.  Then  while  I  gramme  weight  (11,200 
cub.  centims.)  of  hydrogen  and  8  grammes  (5,600  c.  c.)  of 
oxygen  are  set  free  in  the  voltameter,  31*5  grammes  of  cuppar 
will  be  deposited  in  each  cell  of  the  battery,  and  (neglecting  loss 
by  local  action),  32*5  grammes  of  zinc  will  be  dissolved  in  each 
cell. 

220.  It  will  therefore  bs  evident  that  the  electrolytic 
cell  is  the  con-verse  of  the  \oltaic  cell.     The  chemical  \\ork 
done  in  the  voltaic  cell  furnishes  the  energy  of  the  cunent 
which  that  cell  sets  up  in  the  circuit.      In  the  electrolytic 
cell  chemical  work  is  performed,  the  necessary  energy 
being   furnished  by  the   current  of  electricity  which   is 
sent  into  the  cell  from  an  independent  batteiy  or  other 
source. 

A  theory  of  electrolysis,  and  some  examples  of  its 
application,  are  given  in  Chapter  XXXVIII.  on  Electro- 
chemistry. 


LESSON  XIX. — Physical  and  Physiological  Effects  of 
the  Current* 

221.  Molecular  Actions. — Metal  conductors,  when 
subjected  to  the  prolonged  action  of  currents,  undergo 
slow  molecular  changes.  Wires  cf  copper  and  brass 
gradually  become  brittle  under  its  influence.  During 
the  passage  of  the  current  through  metallic  wires  their 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  181 

cohesion  is  temporarily  lessened,  and  there  also  appears 
to  be  a  decrease  in  their  coefficient  of  elasticity.  It  was 
thought  by  Edlund  that  a  definite  elongation  could  be 
observed  in  strained  wires  when  a  current  was  passed 
through  them ;  but  it  has  not  yet  been  satisfactorily 
shown  that  this  elongation  is  independent  of  the  elonga- 
tion due  to  the  heating  of  the  wire  owing  to  the  resistance 
it  opposes  to  the  current. 

222.  Electric  Osmose. — Porret  observed  that  if  a 
strong  current  is  led  into  certain  liquids,  as  if  to  electro- 
lyse them,  a  porous  partition  being  placed  between  the 
electrodes,  the  current  mechanically  carries  part  of  the 
liquid  through  the  porous  diaphragm,  so  that  the  liquid 
is  forced  up  to  a  higher  level  on  one  side  than   on  the 
other.     This  phenomenon,  known  as  electric  osmose,  is 
most  manifest  when  badly  conducting  liquids,  such  as 
alcohol  and  bisulphide  of  carbon,  are  used.     The  transfer 
through  the  diaphragm  takes  place  in  the  direction  of 
the  current ;  that  is  to  say,  the  liquid  is  higher  about 
the  kathode  than  round  the  anode. 

223.  Electric     Distillation.  —  Closely    connected 
with  the  preceding  phenomenon  is  that  of  the  electric 
distillatien  of  liquids.      It  was  noticed  by  Beccaria  that 
an  electrified  liquid  evaporated  more  rapidly  than  one 
not  electrified.     Gernez  has   recently  shown  that    in  a 
bent  closed  tube,  containing  two  portions  of  liquid,  one 
of  which  is  made  highly  +  and  the  other  highly  —  ,  the 
liquid  passes  over  from  +  to  -       This  apparent  distilla- 
tion is  not  due  to  difference  of  temperature,  nor  does  it 
depend  on  the  extent  of  surface  exposed,  but  is  effected 
by  a  slow  creeping  of  the  liquid  along  the  interior  surface 
of  the  glass  tubes.     Bad  conductors,  such  as  turpentine, 
do  not  thus  pass  over. 

224.  Diaphragm    Currents. — Professor    Quincke 
discovered  that  a  current  is  set  up  in  a  liquid  when  it  is 
forced  by  pressure  through  a  porous  diaphragm.     This 
phenomenon  may  be  regarded  as  the  converse  of  electric 


i8a  ELEMENTARY  LESSONS  ON      [CHAP.  III. 

osmose.  The  E.M.F.  of  the  current  varies  with  the 
pressure  and  with  the  nature  of  the  diaphragm.  When 
water  was  forced  at  a  pressure  of  one  atmosphere 
through  sulphur,  the  difference  of  potential  was  over  9 
volts.  With  diaphragms  of  porcelain  and  bladder  the 
differences  were  only  -35  and  -01  volts  respectively. 

225.  Electro-Capillary  Phenomena. — If  a  hori- 
zontal glass  tube,  turned  up  at  the  ends,  be  filled  with 
dilute  acid,  and  a  single  drop  of  mercury  be  placed  at 
about  the  middle  of  the  tube,  the  passage  of  a  current 
through  the  tube  will  cause  the  drop  to  move  along 
towards  the  negative  pole.  It  is  believed  that  the 
liberation  of  very  small  quantities  of  gas  by  electrolysis  at 
the  surface  where  the  mercury  and  acid  meet  alters  the 
surface-tension  very  considerably,  and  thus  a  movement 
results  from  the  capillary  forces.  Lippmann,  Dewar. 
and  others,  have  constructed  upon  this  principle  capillary 
electrometer s,  in  which  the  pressure  of  a  column  of  liquid 
is  made  to  balance  the  electro-capillary  force  exerted  at 
the  surface  of  contact  of  mercury  and  dilute  acid,  the 
electro-capillary  force  being  nearly  proportional  to  the 
electromotive-force  when  this  does  not  exceed  one  volt. 
Fig.  93  shows  the  capillary  electrometer  of  Dewar. 
A  glass  tube  rests  horizontally  between  two  glass  dishes 
in  which  holes  have  been  bored  to  receive  the  ends  of 


Fig.  93. 

the  tube.  It  is  filled  with  mercury,  and  a  single  drop 
of  dilute  acid  is  placed  in  the  tube.  Platinum  wires  to 
serve  as  electrodes  dip  into  the  mercury  in  the  dishes. 
An  E.M.F.  of  only  ,$T  volt  suffices  to  produce  a  measure- 


CHAP,  in.]   ELECTRICITY  AND  MAGNETISM.  183 

able   displacement  of  the   drop.      The  direction  of  the 
displacement  varies  with  that  of  the  current. 

226.  Physiological  Actions. —  Currents   of    elec- 
tricity passed  through   the  limbs   affect  the  nerves  with 
certain   painful   sensations,    and    cause   the    muscles   to 
undergo  involuntary  contractions.      The  sudden  rush  of 
even   a   small  charge   of  electricity  from   a   Leyden  jar 
charged  to  a  high  potential,  or  from  an   induction   coil 
(see  Fig.  148),  gives  a  sharp  and   painful  shock  to  the 
system.      The  current  from  a  few  strong  Grove's  cells, 
conveyed   through  the  body  by  grasping  the  terminals 
with   moistened   hands,  gives   a  very  different   kind   of 
sensation,  not  at  all  agreeable,  of  a  prickling  in  the  joints 
of   the    arms    and    shoulders,    but    not    producing    any 
spasmodic    contractions,  except    it    be    in     nervous    or 
weakly  persons,  at  the  sudden   making  or  breaking   of 
the  circuit.     The  difference  between  the  two  cases  lies 
in  the  fact  that  the  tissues  of  the  body  offer  a  very  con- 
siderable resistance,  and  that  the  difference  of  potential 
in   the  former  case  may  be  many  thousands  of  volts  ; 
hence,    though    the    actual    quantity   stored    up   in    the 
Leyden  jar  is  very  small,  its  very  high  E.M.F.  enables 
it  at  once   to  overcome   the  resistance.       The   battery, 
although  it   might,  when  working  through  a  good  con- 
ductor," afford  in  one  second  a  thousand  times  as  much 
electricity,  cannot,  when   working  through  the  high  re- 
sistance of  the  body,  transmit  more  than  a  small  fraction, 
owing  to  its  limited  E.M.F. 

After  the  discovery  of  the  shock  of  the  Leyden  jar  by 
Cunseus  in  1745  many  experiments  were  tried.  Louis 
XV.  of  France  caused  an  electric  shock  from  a  battery  of 
Leyden  jars  to  be  administered  to  700  Carthusian  monks 
joined  hand  in  hand,  with  prodigious  effect.  Franklin 
killed  a  turkey  by  a  shock  from  a  Leyden  jar. 

227.  In    1752   Sulzer  remarked  that  "  if  you  join  two 
pieces  of  lead   and  silver,   and  then  lay  them  upon  the 
tongue,  you  will  notice  a  certain  taste  resembling  that  of 


i«4  ELEMENTARY  LESSONS  ON      [CHAP.  in. 

; V ; • _,__ 

green  vitriol,  while  each  piece  "apart  produces  no  such 
sensation. "  This  galvanic  tastel  not  then  suspected 
to  have  any  Connection  with  electricity,  may  be  ex- 
perienced by  placing  a  silver  coin  on  the  tongue  and  a 
steel  pen  under  it,  the  edges  of  them  being  then  brought 
into  metallic  contact.  The  same  taste  is  noticed  if  the 
two  wires  from  the  poles  of  a  voltaic  cell  are  placed  in 
contact  with  the  tongue. 

228.  Ritter  discovered  that  a  feeble  current  trans- 
mitted through  the  eyeball  produces  the  sensation  as  of 
a  bright  yfau/J  of  liglit  .by  its  sudden  stimulation  of  the 
optic  nerve.  A  stronger  current  transmitted  by  means 
of  moistened  conductors  attached  to  the  batter)'  terminals 
gave  a  sensation  of  blue  and  green  colours  in  flowing 
between  the  forehead  and  the  hand.  Helmholtz,  re- 
peating this  experiment,  observed  only  a  wild  rush  of 
colour.  Dr.  Hunter  saw  flashes  of  light  when  a  piece 
of  metal  placed  under  the  tongue  was  touched  against 
another  which  touched  the  moist  tissues  of  the  eye. 
Vblta  and  Ritter  heard  musical  sounds  when  a  current 
was  passed  through  the  ears  :  and  Humboldt  found  a 
sensation  to  be  produced  in  the  organs  of  smell  when  a 
current  was  passed  from  the  nostril  to  the  soft  palate. 
Each  of  the  specialised  senses  can  be  stimulated  into 
activity  by  the  current.  Man  possesses  no  specialised 
sense  for  the  perception  of  electrical  forces,  as  he  does 
for  light  and  for  sound  ;  but  there  is  no  reason  for  denying 
the  possibility  that  some  of  the  lower  creatures  may  be 
endowed  with  a  special  electrical  sense. 

The  following  experiment  shows  the  effect  of  feeble 
currents  on  cold-blooded  creatures. '  If  a  copper  (or  silver) 
coin  be  laid  on  a  piece  of  sheet  zinc,  and  a  common 
garden  snail  be  set  to  -  crawl  •  over  the  zinc,  directly 
it  comes  into  contact  with  the  copper  it  will  suddenly 
jmll  in  its  horns,  and  shrink  in  its  body.  If  it  is  set  to 
crawl  over  two  copper  wires,  which  are  then  placed  in 
contact  with  a  feeble  voltaic  cell,  it  immediately  an- 


CHAP,  III.]  ELECTRICITY  AND  MAGNETISM. 


185 


nounces  the   establishment  of  a   current  by   a   similar 
contraction.1 

229.  Muscular  Contractions. — In  1678  Swam- 
merdam  showed  to  the  Grand  Duke  of  Tuscany  that  when 
a  portion  of  muscle  of  a  frog's  leg  hanging  by  a  thread  of 
nerve  bound  with  silver  wire  was  held  over  a  copper 
support,  so  that  both  nerve  and  wire  touched  the  copper, 
the  muscle  immediately  contracted.  More  than  a  cen- 


Fig.  94. 

tury  later  Galvani's  attention  was  drawn  to  the  subject 
by  his  observation  of  spasmodic  contractions  in  the  legs 
of  freshly-killed  frogs  under  the  influence  of  the  "  return- 
shock  "  experienced  every  time  a  neighbouring  electric 
machine  was  discharged.  Unaware  of  Swammerdam's 
experiment,  he  discovered  in  1786  the  fact  (alluded  to  in 

1  Tt  will  scarcely  be  credited  that  a  certain  Jules  A'lix  once  seriously  pro- 
posed a  system  of  telegraphy  based  on  this  physiological  phenomenon. 


1 86  ELEMENTARY  LESSONS  ON      [CHAP,  ill 

Art.  148  as  leading  ultimately  to  the  discovery  of  tne 
Voltaic  Pile)  that  when  nerve  and  muscle  touch  two 
dissimilar  metals  in  contact  with  one  another  a  con- 
traction of  the  muscle  takes  place.  The  limbs  of  the 
frog,  prepared  as  directed  by  Galvani,  are  shown  in  Fig. 
94.  After  the  animal  has  been  killed  the  hind  limbs 
are  detached  and  skinned  ;  the  crural  nerves  and  their 
attachments  to  the  lumbar  vertebras  remaining.  For 
some  hours  after  death  the  limbs  retain  their  contractile 
power.  The  frog's  limbs  thus  prepared  form  an  ex- 
cessively delicate  galvanosccpe :  with  them,  for  example, 
the  excessively  delicate  induction-currents  of  the  tele- 
phone (Lesson  XL.)  can  be  shown,  though  the  most 
sensitive  galvanometers  barely  detect  them.  Galvani 
and  Aldini  proved  that  other  creatures  undergo  like 
effects.  With  a  pile  of  100  pairs  Aldini  experimented 
on  newly  killed  sheep,  oxen,  and  rabbits,  and  found  them 
to  suffer  spasmodic  muscular  contractions.  Humboldt 
proved  the  same  on  fishes  ;  and  Zanotti,  by  sending  a 
current  through  a  newly  killed  grasshopper,  caused  it  to 
emit  its  familiar  chirp.  Aldini,  and  later  Dr.  Ure  oi 
Glasgow,  experimented  on  the  bodies  of  executed  crimi- 
nals, with  a  success  terrible  to  behold.  The  facial 
muscles  underwent  horrible  contortions,  and  the  chest 
heaved  with  the  contraction  of  the  diaphragm.  This 
has  suggested  the  employment  of  electric  currents  as  an 
adjunct  in  reviving  persons  who  have  been  drowned,  the 
contraction  of  the  muscles  of  the  chest  serving  to  start 
respiration  into  activity.  The  small  muscles  attached 
to  the  roots  of  the  hairs  of  the  head  appear  to  be 
be  markedly  sensitive  to  electrical  conditions  from  the 
readiness  with  which  electrification '  causes  the  hair  to 
stand  on  end. 

23O.  Conditions  of  Muscular  Contraction. — To 
produce  muscular  contraction  the  current  must  traverse 
a  portion  of  the  nerve  longitudinally.  In  a  freshly  pre- 
pared frog  the  current  causes  a  contraction  only  momen- 


CHAP,  in.)  ELECTRICITY  AND  MAGNETISM.  187 

tarily  when  the  circuit  is  made  or  broken.  A  rapidly 
interrupted  current  will  induce  a  second  contraction 
before  the  first  has  had  time  to  pass  off,  and  the  muscle 
may  exhibit  thus  a  continuous  contraction,  resembling 
tetanus.  The  prepared  frog  after  a  short  time  becomes 
less  sensitive,  and  a  "  direct  "  current  (that  is  to  say,  one 
passing  along  the  nerve  in  the  direction  from  the  brain 
to  the  muscle)  only  produces  an  effect  when  circuit  is 
made,  while  an  "  inverse "  current  only  produces  an 
effect  when  the  circuit  is  broken.  Matteucci,  who 
observed  this,  also  discovered  by  experiments  on  living 
animals  that  there  is  a  distinction  between  the  con- 
ductivity of  sensory  and  motor  nerves,  —  a  "direct", 
current  affecting  the  motor  nerves  on  making  the 
circuit,  and  the  sensory  nerves  on  breaking  it  ;  while 
an  "  inverse  "  current  produced  inverse  results.  Little 
is,  however,  yet  known  of  the  conditions  of  con- 
ductivity of  the  matter  of  the  nerves  ;  they  conduct 
better  than  muscular  tissue,  cartilage,  or  bone  ;  but  oi 
all  substances  in  the  body  the  blood  conducts  best. 
Powerful  currents  doubtless  electrolyse  the  blood  to 
some  extent,  coagulating  it  and  the  albumin  it  contains. 
The  power  of  contracting  under  the  influence  of  the 
current  appears  to  be  a  distinguishing  property  of 
protoplasm  \\herever  it  occurs.  The  amoeba,  the 
most  structureless  of  organisms,  suffers  contractions. 
Ritter  discovered  that  the  sensitive  plant  shuts  up  when 
electrified,  and  Burdon  Sanderson  has  shown  that  this 
property  extends  to  other  vegetables,  being  exhibited  by 
the  carnivorous  plant,  the  Dioncea  or  Venus'  Fly  Trap. 

231.  Animal  Electricity. — Although,  in  his  later 
writings  at  least,  Galvani  admitted  that  the  electricity 
thus  operating  arose  from  the  metals  employed,  he 
insisted  on  the  existence  of  an  animal  electricity  resident 
in  the  muscular  and  nervous  structures.  He  showed 
that  contractions  could  be  produced  without  using  any 
jnetals  at  all  by  merely  touching  a  nerve  at  two  different 


i88  ELEMENTARY  LESSONS  ON      [CHAP.  IIL 

points  along  its  length  with  a  morsel  of  muscle  cut  Irom 
a  living  frog  ;  and  that  a  conductor  of  one  metal  when 
joining  a  nerve  to  a  muscle  also  sufficed  to  cause  con- 
traction  in   the   latter.       Galvani    and   Aldini    regarded 
these    facts    as    a    disproof  of  Volta's    contact -theory. 
Volta    regarded    them    as    proving    that    the    contact 
between   nerve   and   muscle   itself  produced  (as   in  the 
case  of  two  dissimilar   metals)  opposite  electrical  con- 
ditions.     Nobili,  later,  showed  that  when  the  nerve  and 
the  muscle  of  the  frog  were  respectively  connected  by  a 
water -contact  with  the  terminals  of  a  delicate  galvan- 
ometer, a  current  is  produced  which  lasts  several  hours  : 
he   even   arranged    a  number   of  frogs'   legs   in   series, 
like  the  cells  of  a  battery,  and  thus  increased  the  current. 
Matteucci  showed  that  through  the  muscle  alone  there  is 
an  electromotive-force.      Du  Bois  Reymond  has  shown 
that  if  the  end  of  a  muscle  be  cut  across,  the  ends  of  the 
muscular  fibres  of  the  transverse  section  are  negative, 
and  the  sides  of  the  muscular  fibres  are  positive,  and 
that  this  difference  of  potential  will  produce  a  current 
even  while  the  muscle  is  at  rest.     To  demonstrate  this 
he  employed  a  fine  astatic  galvanometer  with  20,000 
turns  of  wire  in  its  coils ;  and  to  obviate  errors  arising 
from  the  contact  of  the  ends  of  the  wires  with  the  tissues 
unpolarisable  electrodes  were   used,  made    by   plunging 
terminal  zinc  points  into  a  saturated  solution  of  sulphate 
of  zinc,  contained  in  a  fine  glass  tube,  the  end  of  which 
was  stopped  with  a  porous  plug  of  moistened  china  clay. 
The    contraction    of    muscles    also    produces    currents. 
These  Du  Bois  Reymond  obtained  from  his  own  muscles 
by  dipping  the  tips   of  his  fore -fingers  into   two  cups 
of    salt    water    communicating    with    the    galvanometer 
terminals.     A   sudden    contraction    of    the    muscles    of 
either    arm    produced    a    current    from    the    contracted 
toward   the   uncontracterl   muscles.      Dewar   has   shown 
that    when    light   falls   upon   the   retina   of  the   eye   an 
electric  current  is  set  up  in  the  optic  nerve. 


CHAP,  in.]  ELECTRICITY.  AND  MAGNETISM.  189 

232.  Medical  Applications.  —  Electric  currents 
have  been  successfully  employed  as  an  adjunct  in 
restoring  persons  rescued  from  drowning ;  the  contrac- 
tion of  the  diaphragm  and  chest  muscles  serving  to  start 
respiration.  Since  the  discovery  of  the  Leyden  jar 
many  attempts  have  been  made  to  establish  an  electrical 
medical  treatment.  Discontinuous  currents,  particularly 
those  furnished  by  small  induction-coils  and  magneto- 
electric  machines,  are  employed  by  practitioners  to 
stimulate  the  nerves  in  paralysis  and  other  affections. 
Electric  currents  should  not  be  used  at  all  except  with 
great  care,  and  under  the  direction  of  regularly  trained 
surgeons.1 

J  It  is  not  out  of  place  to  enter  an  earnest  caution  on  this  head  against  the 
numerous  quacic  doctors  who  deceive  the  un wary  with  magnetic  and 
galvanic  "appliances."  In  many  cases  these  much-advertised  shams  have 
done  incalculable  harm :  in  the  very  few  cases  where  «ome  fancied  good  has 
accrued  the  curative  agent  is  probably  not  magnetism,  but  flannel  1 


190  ELEMENTARY  LESSONS  ON      [CHAP.  IV, 


Stcoirt, 

CHAPTER   IV. 

ELECTROSTATICS. 

LESSON  XX. — Theory  oj  Potential. 

233.  By  the  Lessons  in  Chapter  I.  the  student  will 
have  obtained  some  elementary  notions  upon  the  exist- 
ence and  measurement  of  definite  quantities  of  electricity. 
In  the  present  Lesson,  which  is  both  one  of  the  hardest 
andv  one  of  the  most  important  to  the  beginner,  and 
which  he  must  therefore  study  the  more  carefully,  the 
laws  which  concern  the  magnitude  of  electrical  quantities 
and  their  measurement  are  more  fully  explained.  .  In  no 
branch  of  knowledge  is  it  more  true  than  in  electricity, 
that  '•  science  is  measurement."     That  part  of  the  science 
of    electricity    which    deals    with    the    measurement    of 
charges   of  electricity  is  called   Electrostatica     We 
shall  begin  by  discussing  first  the  simple  laws  of  electric 
force,  which  were  brought   to   light  in   Chapter. I.   by 
simple  experimental  means. 

234.  First    Law    of    Electrostatics. — Electric 
charges   of  similar  sign  repel  one  another^  hut  electric 
charges  of  opposite  signs  attract  one  another.     The  funda- 
mental facts  expressed  in  this  Law  were  fully  explained 
in    Lesson    I.      Though    familiar    to  '  the    student,   and 
apparently  simple,  these  facts  require  for  their  complete 
explanation  the  aid  of  advanced  mathematical  analysis, 
They  will  here  be  treated  as  &.mple  facts  of  observation. 


CHAP,  iv.}  ELECTRICITY  AND  MAGNETISM.  191 

235.  Second  Law  of  Electrostatics.  —  The  force 
exerted  between  two  charges  of  electricity  (supposing  them 
to  be  collected  at  points  or  on  two  small  spheres),  is 
directly  proportional  to  their  product,  and  inversely 
proportional  to  the  square  of  the  distance  between  them. 
This  law,  discovered  by  Coulomb,  and  called  Coulomb's 
Law,  was  briefly  alluded  to  (on  page  16)  in  the  account 
of  experiments  made  with  the  torsion  -balance  -,  and 
examples  were  there  given  in  illustration  of  both  parts  of 
the  law.  We  saw,  too,  that  a  similar  law  held  good  for 
the  forces  exerted  between  two  magnet  poles.  Coulomb 
applied  also  the  method  of  oscillations  to  verify  the 
indications  of  the  torsion-balance  and  found  the  results 
entirely  confirmed.  We  may  express  the  two  clauses  of 
Coulomb's  law,  in  the  following  symbolic  manner.  Let 
/stand  for  the  force,  q  for  the  quantity  of  electricity  in 
one  of  the  two  charges,  and  q'  for  that  of  the  other 
charge,  and  let  d  stand  for  the  distance  between  them. 
Then, 

(i.)  /is  proportional  to^  x  ^ 

and  (2.)  /is  proportional  td-^- 

These  two  expressions  may  be  combined  into  one  ; 
and  it  is  most  convenient  so  to  choose  our  units  or 
standards  of  measurement  that  we  may  write  our  symbols 
as  an  equation  :  — 


236.  Unit  of  Electric  Quantity.  —  If  we  are,  how. 
ever,  to  write  this  as  an  equality,  it  is  clear  that  we 
must  choose  our  unit  of  electricity  in  accordance  with 
the  units  already  fixed  for  measuring  force  and  distance. 
All  electricians  are  now  virtually  agreed  in  adopting  a 
system  which  is  based  upon  three  fundamental  units  : 
viz.,  the  Centimetre  for  a  unit  of  length;  the  Gramme 
for  a  unit  of  mass  ,  the  Second  for  a  unit  of  time.  AJJ 


192  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

other  units  can  be  derived  from  these,  as  is  explained 
in  the  Note  at  the  end  of  this  Lesson.  Now,  amongst 
the  derived  units  of  this  system  is  the  unit  of  force, 
named  the  Dyne,  which  is  that  force  which,  acting  for 
one  second  on  a  mass  of  one  gramme,  imparts  to  it 
a  velocity  of  one  centimetre  per  second.  Taking  the 
dyne  then  as  the  unit  of  force,  and  the  centimetre  as 
the  unit  of  length  (or  distance),  we  must  find  a  unit  of 
electric  quantity  to  agree  with  these  in  our  equation. 
It  is  quite  clear  that  if  q,  /,  and  d  were  each  made  equal 
to  i  (that  is,  if  we  took  two  charges  of  value  I  each, 
and  placed  them  one  centimetre  apart),  the  value  of 

q  X  q  I  X  I 

~j*~  would  be          •   , which  is  equal  to  i.     Hence  we 

adopt,  as  our  Definition  of  a  Unit  of  Electricity,  the 
following,  which  we  briefly  gave  at  the  end  of  Lesson  II. 
One  Unit  of  Electricity  is  that  quantity  which,  when  placed 
at  a  distance  of  one  centimetre  (in  air)  from  a  similar  and 
equal  quantity,  repels  it  with  a  force  of  one  dyne. 

An  example  will  aid  the  student  to  understand  the 
application  of  Coulomb's  law. 

EXAMPLE. — Two  small  spheres,  charged  respectively  with 
6  units  and  8  units  of  +  electricity,  are  placed  4 
centimetres  apart ;  find  what  force  they  exert  on  one 

another.     By  the  formula,  /  =  ^a- ,  we   find  /  = 

—5-  =  ^  =   3  dynes.     Examples  for  the  student 
are  given  in  the  Questions  at  the  end  of  the  Book. 

The  force  in  the  above  example  would  clearly  be  a  force 
of  repulsion.  Had  one  of  these  charges  been  negative, 
the  product  q  x  q'  would  have  had  a  -  value,  and  the 
answer  would  have  come  out  as  minus  3  dynes.  The 
presence  of  the  negative  sign,  therefore,  prefixed  to  a 
force,  will  indicate  that  it  is  a  force  of  attraction,  whilst 
the  +  sign  would  signify  a  force  of  repulsion. 

237.  Potential. — We  must  next  define  the  term 
potential,  as  applied  to  electric  forces  ;  but  to  make 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM.  193 

the  meaning  plain  a  little  preliminary  explanation  is 
necessary.  Suppose  we  had  a  charge  of  +  electricity 
on  a  small  insulated  sphere  A  (See  Fig.  95),  placed  by 
itself  and  far  removed  from  all  other  electrical  charges 
and  electrical  conductors.  If  we  were  to  bring  another 
body  B  near  it,  charged  also  with  +  electricity,  A  would 
repel  B.  But  the  repelling  force  would  depend  on  the 
quantity  of  the  new  charge,  and  on  the  distance  at  which 
it  was  placed.  Suppose  the  new  charge  thus  brought 

A  P  Q  J9"  B' 

~\.____  ---------------  Q  . 


Fig.  95- 

near  to  be  one  unit  of  +  electricity  ;  when  B  was  a  long 
way  off  it  would  be  repelled  with  a  very  slight  force,  and 
very  little  work  need  be  expended  in  bringing  it  up 
nearer  against  the  repelling  forces  exerted  by  A  ;  but  as 
B  was  brought  nearer  and  nearer  to  A,  the  repelling 
force  would  grow  greater  and  greater,  and  more  and 
more  work  would  have  to  be  done  against  these  oppos- 
ing forces  in  bringing  up  B.  Suppose  that  we  had 
begun  at  an  infinite  distance  away,  and  that  we  pushed 
up  our  little  test  charge  B  from  B'  to  B"  and  then  to  Q, 
and  so  finally  moved  it  up  to  the  point  P,  against  the 
opposing  forces  exerted  by  A,  we  should  have  h2d  to 
spend  a  certain  amount  of  work;  that  work  represents 
the  potential^  at  the  point  P  due  to  A.  For  the  follow- 
ing is  the  definition  of  electrostatic  potential:  —  The 
potential  at  any.  point  is  the  work  that  must  be  spent 

1  In  its  widest  meaning  the  term  "potential"  must  be  understood  as 
"power  to  do  work."  For  if  we  have  to  do  a  certain  quantity  of  work 
against  the  repelling  force  of  a  charge  in  bringing  up  a  unit  of  electricity 
from  an  infinite  distance,  just  so  much  work  has  the  charge  power  to  do,  for 
it  will  spend  an  exactly  equal  amount  of  work  in  pushing  the  unit  of  electri- 
city back  to  an  infinite  distance.  If  we  lift  a  pound  five  feet  high  against 
the  force  of  gravity,  the  weight  of  the  pound  can  in  turn  do  five  foot-pounds 
of  work  in  falling  back  to  the  ground.  See  the  Lesson  on  Energy  in  Pro- 
fessor Balfour  Stewart's  Lessons  ia  Elementary  Physics. 

O 


194  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

i    —  —  ~~  -  •  - 

Upon  a  tint  I  of  positive  electricity  in  bringing  it  up  to 
that  point  from  an  infinite  distance.  Had  the  charge  on 
A  been  a  -  charge,  the  force  would  have  been  one  of 
attraction,  in  which  case  we  should  have  theoretically  to 
measure  the  potential  at  P,  either  by  the  opposite 
process  of  placing  there  a  +  unit,  and  then  removing  it 
to  an  infinite  distance  against  the  attractive  forces,  or 
else  by  measuring  the  amount  of  work  which  would  be 
done  by  a  -f  unit  in  being  attracted  up  to  P  from  an 
infinite  distance. 

It  can  be  shown  that  where  there  are  more  electrified 
bodies  than  one  to  be  considered,  the  potential  due  to 
them  at  any  point  is  the  sum  of  the  potentials  (at  that 
point)  of  each  one  taken  separately. 

238.  It  can  also  be  shown  that  the  potential  at  a 
point  P,  near  an  electrified  particle  A,  is  equal  to  the 
quantity  of  electricity  at  A  divided  by  the  distance 
between  A  and  P.  Or,  if  the  quantity  be  called  g,  and 

the  distance   r,   the   potential   is  -£.*     If  there  are  a 

r 

number  of  electrified  particles  at  different  distances 
from  P,  the  separate  values  of  the  potential  -£  due  to 

r 

each  electrified  particle  separately  can  be  found,  and 
therefore  the  potential  at  P  can  be  found  by  dividing  the 
quantity  of  each  charge  by  its  distance  from  the  point  P, 
and  then  adding  up  together  the  separate  amounts  so 
obtained.  The  symbol  V  is  generally  used  to  represent 
potential.  The  potential  at  point  P  we  will  call  VP,  then 


or  VP  =   2f; 
r 

This  expression  2  i-  represents  the  work  done  on  01 

*  The  complete  proof  would  require  an  elementary  application  of  the 
integral  cakulus,  but  an  easy  geometrical  demonstration,  sufficient  for 
present  purposes,  is  given  below. 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM.  195 

by  a  unit  of  +  electricity  when  moved  up  to  the  given 
point  P  from  an  infinite  distance,  according  as  the 
potential  at  P  is  positive  or  negative. 

Proof. — First  detfrritine  the  difference  of  potential  between 
point  P  and  point  Q  due  to  a  charge  .of  electricity  q  on  a  small 
sphere  at  A. 


Fig.  96. 

Call  distance  AP  =  r,  and  AQ  =  r1.  Then  PQ  = 
r1  —  r.  The  difference  of  potential  between  Q  and  P  is  the 
work  done  in  moving  a  +  unit  from  Q  to  F  against  the  force  ; 
and  since 

work  =  (average)  force  x  distance  through  which  it 
is  overcome 

VP- VQ  =  /(/-^. 

The  force  at  P  exerted  by  q  on  a  +  unit  =    •%, 
and  the  force  at  Q  exerted  by  q  on  a  +  unit  =   -^y. 

Suppose  now  that  the  distance  PQ  be  divided  info  any 
number  («)  of  equal  parts  rrlt  r^r^  /y,, '*->*• 

The  force  at  r  =   •£. 

•  •    'i  =   fl  '   '    '   '   etc- 
;i 

Now  since  r^  may  be  made  as  close  to  r  as  we  choose,  if  we 
only  take  tr  a  large  enough  number,  we  shall  commit  no  serious 
error  in  supposing  that  r  x  r,  is  a  fair  mean  between  r*  and 
r,!;  hence  we  may  assume  the,  avtragt  force  over  the  short 


196  ELEMENTARY  LESSONS  ON       [CHAP  rv, 


Hence  the  work  done  in  passing  from  rl  to  r  will  be 


On  a  similar  assumption,  the  work  done  in  passing  from  rt 
to  rlt  will  be 

=•  q  (  —  -     ;  )  »  and  that  done  from  rs  to  ra  will  be 

=  ^  (  —  —  —  )>  etc.,  giving  us  n  equations,  of  which 
\  r^         r^f 

the  last  will  be  the  work  done  in  passing  from  r  to  rn_, 


Adding  up  all  these  portions  of  the  work,  the  intermediate 
values  of  r  cancel  out,  and  we  get  for  the  work  done  in  pass 
ing  from  Q  to  P 

VP  -V,=,(f  --£>) 

Next  suppose  Q  to  be  an  infinite  distance    from  A.     Here 
r   =  infinity,  and    -7-    =    o.       In    that    case    the   equation 

becomes 

V      =    $- 

p  r 

If  instead  of  one  quantity   of    electricity  f,  there  were  a 
number  of  electrified  particles  having  charges  g',  y",  tf*  .  .  .  . 

etc.,  at  distances  of  r\  r",  t'" etc.,  respectively  from 

P,  then 


V     = 


r 


q 
Vp     =    2   1         which  was  to  be  proved. 

239.  Zero  Potential — At  a  place  infinitely  distant 
from  all  electrified  bodies  there  would  be  no  electric 
forces  and  the  potential  would  be  zero.  For  purposes 
of  convenience  it  is,  however,  usual  to  consider  the 
potential  of  the  earth  for  the  time  being  as  an  arbitrary 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  107 

zero,  just  as  it  is  convenient  to  consider  "  sea-level "  as 
a  zero  from  which  to  measure  heights  or  depths. 

24O.  Difference  of  Potentials. — Since  potential 
represents  the  work  that  must  be  done  on  a  +  unit  in 
bringing  it  up  from  an  infinite  distance,  the  difference 
of  potential  between  two  points  is  the  work  to  be  done  on 
o r  by  a  +  unit  of  electricity  in  carrying  it  from  one  point 
to  the  other.  Thus  if  VP  represents  the  potential  at  P, 
and  VQ  the  potential  at  another  point  Q,  the  difference 
of  potentials  VP  —  VQ  denotes  the  work  done  in  moving 
up  the  +  unit  from  Q  to  P.  It  is  to  be  noted  that  since 
this  value  depends  only  on  the  values  of  the  potential 
at  P  and  at  Q,  and  not  on  the  values  of  the  potential  at 
intermediate  points,  the  work  done  will  be  the  same, 
whatever  the  path  along  which  the  particle  moves  from 
Q  to  P.  In  the  same  way  it  is  true  that  the  expenditure 
of  energy  in  lifting  a  pound  against  the  earth's  attraction 
from  one  point,  to  another  on  a  higher  level,  will  be  the 
same  whatever  the  path  along  which  the  pound  is  lifted. 
24L  Electric  Force. — The  definition  of  "  work  "  is 
the  product  of  the  force  overcome  into  the  distance 
through  which  the  force  is  overcome,  or  work  =  force 
x  distance  through  which  it  is  overcome. 

Hence,  if  the  difference  of  potential  between  two 
points  is  the  work  done  in  moving  up  our  +  unit  from 
one  point  to  the  other,  it  follows  that  the  average  electric 
force  between  those  points  will  be  found  by  dividing 
the  work  so  done  by  the  distance  between  the  points : 

or    p  ~    Q  =/  (the  average  electric  force  along  the  line 

PQ).  The  (average)  electric  force  is  therefore  the  rate 
of  change  of  potential  per  unit  of  length.  If  P  and  Q 
are  near  together  the  force  will  be  practically  uniform 
between  P  and  Q. 

242.  Bquipotential  Surfaces. — A  charge  of  elec- 
tricity collected  on  a  small  sphere  acts  on  external 
bodies  as  if  the  charge  were  all  collected  into  one  point 


198  ELEMENTARY  LESSONS  ON      [CHAF.  iv. 

at  its  centre.1  We  have  seen  that  the  force  exerted  by 
such  a  charge  falls  off  at  a  distance  from  the  ball,  the 
force  becoming  less  and  less  as  the  square  of  the 
distance  increases.  But  the  force  is  the  same  in 
amount  at  all  points  equally  distant  from  the  small  charged 
sphere.  And  the  potential  is  the  same  at  all  points 
that  are  equally  distant  from  the  charged  sphere.  "If,  in 
Fig.  96,  the  point  A  represents  the  sphere  charged  with 
q  units  of  electricity,  then  the  potential  at  P,  which  we 

will  call  VP,  will  be  equal  to  -,  where  r  is  the  distance 
from  A  to  P.  But  if  we  take  any  other  point  at  the 
same  distance  from  A  its  potential  will  also  be  -4  Now 

all  the  points  that  are  the  same  distance  from  A  as 
P  is,  will  be  found  to  lie  upon  the, surface  of  a  sphere 
whose  centre  is  at  A,  and  which  is  represented  by  the 
circle  drawn  through  P,  in  Fig.  97.  All  round  this  circle 
the  potential  will  have  equal  values ;  hence  this  circle 
represents  an  equipotential  surface.  The  work  to 
be  done  in  bringing  up  a  +  unit  from  .an  infinite  distance 
will  be  the  same,  no  matter  what  point  of  this  equi- 
potential surface  it  is  brought  to,. and  to  move  it  about 
from  one  point  to  another  in  the  equipotential  surface 
requires  no  further  overcoming  of  the  electrical  forces, 
and  involves  therefore  no'  further  expenditure  of  work. 
At  another  distance,  say  at  the  point  Q,  the  potential 
will  have  another  value,  and  through  this,  point  C 
another  equipotential  surface  may  be  drawn.  Suppos  | 
we  chose  Q  so  far  from  P  that  to  .push  up  a  unit  of  -t 
electricity  against  the  repelling  force  of  A  required  the 
expenditure  of.  just  one  erg  of  work  (for  the  definition 

1  Thq  student  must  be  warned  that  this  ceases  to  be  true  if  other  charges 
are  brought  very  near  to  the  sphere,  for  then  the  electricity  will  no  longer 
be  distributed  uniformly  over  its  surface.  It  is  for  this  reason  that  we  have 
said,  in  describing -the  measurement  of  electrical  forces  with  the  torsion 
balance,  that  "  the  balls  must  be  very  small  in  proportion  to  the  distances 
between  them," 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM. 


199 


of  one  erg  see  the  Note  on  Units  at  the  end  of  this 
lesson) ;  there  will  be  then  unit  difference  of  potential 


A 

• 


F   I" 


Fig.  97. 

between  the  surface  drawn  through  Q  and  that  drawn 
through  P,  and  it  will  require  one  erg  of  work  to  carry 
a  +  unit  from  any  point  on  the  one  surface  to  any  point 
on  the  other.  In  like  manner  we  might  construct  a 
whole  system  of  equipotential  surfaces  about  the  point  A, 
choosing  them  at  such  distances  that  there  should  be 
unit  difference  of  potential  between  each  one  and  the 
next.  The  widths  between  them  would  get  wider  and 
wider,  for,  since  the  force  falls  off  as  you  go  further  from 
A,  you  must,  in  doing  one  erg  of  work,  bring  up  the 
+  unit  through  a  longer  distance  against  the  weaker 
opposing  force. 

The  form  of  the  equipotential  surfaces  about  two  small 
electrified  bodies  placed  near  to  one  another  would  not 
be*  spherical ;  and  around  a  number  of  electrified  bodies 
placed  near  to  one  another  the  equipotential  surfaces 
would  be  highly  irregular  in  form. 

243.  Lines  of  Force. — The  electric  force,  whether 
of  attraction  or  repulsion,  always  acts  across  the  equi- 
potenti?,!  surfaces  in  a  direction  normal  to  the  surface. 
The  lines  which  mark  the  direction  of  the  resultant 
electric  forces  are  sometimes  called  Lines  of  Electric 


xx>  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

Induction.  In  the  case  of  the  single  electrified  sphere 
the  lines  of  force  would  be  straight  lines,  radii  of  the  sys- 
tem of  equipoteritial  spheres.  In  general,  however,  lines 
of  force  are  curved  ;  in  this  case  the  resultant  force  at 
any  point  would  be  in  the  direction  of  tha  tangent  to  the 
curve  at  that  point.  Two  lines  of  force  cannot  cut  one 
another,  for  it  is  impossible  ;  the  resultant  force  at  a  point 
cannot  act  in  two  directions  at  once.  The  positive 
direction  along  a  line  of  force  is  that  direction  in  which 
a  small  body  charged  with  +  electricity  would  be  in> 
pelled  by  the  electric  force,  if  free  to  move.  A  space 
bounded  by  a  number  of  lines  of  force  is  sometimes 
spoken  of  as  a  tube  of  force.  All  the  space,  for  example, 
round  a  small  insulated  electrified  sphere  may  be  re- 
garded as  mapped  out  into  a  number  of  conical  tubes, 
each  having  their  apex  at  the  centre  of  the  sphere.  The 
total  electric  force  exerted  across  any  section  of  a  tube 
of  force  is  constant  wherever  the  section  be  taken. 

244.  Potential  within  a  Closed  Conductor. — 
The  axperiments  related  in  Arts.  29  to  32  prove  most 
convincingly  that  there  is  no  electric  force  inside  a  closed 
conductor.  Now  we  have  shown  above  that  electric 
force  is  the  rate  of  change  of  potential  per  unit  of  length. 
If  there  is  no  electric  force  there  is  no  change  of 
potential.  The  potential  within  a  closed  conductor  (for 
example  a  hollow  sphere)  is  therefore  the  same  all  over 
the  interior ;  the  same  as  the  potential  of  the  surface. 
The  surface  of  a  closed  conductor  is  therefore  necessarily 
an  equipotential  surface.  If  it  were  not  at  one  potential 
there  would  be  a  flow  of  electricity  from  the  higher 
potential  to  the  lower,  which  would  instantaneously 
establish  equilibrium  and  reduce  the  whole  to  one 
potential.  The  power  of  an  electric  system  to  do 
work  does  not  depend  upon  the  accidental  surface- 
density  at  any  one  point.  We  know,  for  instance, 
that  when  an  electrified  body  is  placed  near  an  insulated 
conductor  the  nearer  and  farther  portions  of  that  con-. 


CHAP,  iv.]  ELECTRICITY  AND  MAGNETISM. 


2OI 


ductor  exhibit  induced  charges  of  opposite  kinds.  The 
explanation  of  the  paradox  is  that  in  the  space  round  the 
charged  body  the  potential  is  not  uniform.  Suppose  the 
body  to  have  a  +  charge,  the  potential  near  it  is  higher 
than  in  the  space  farther  away.  The  end  of  the  insulated 
conductor  nearest  to  the  charge  is  in  a  region  of  high 
potential,  while  its  farther  end  is  in  a  region  of  lower 
potential.  It  will,  as  a  whole,  take  a  mean  potential, 
which  will,  relatively  to  the  potential  of  the  surrounding 
medium,  appear  negative  at  the  near  end,  positive  at  the 
far  end. 

245.  Law   of  Inverse  Squares. — An    important 
consequence  follows  from  the  absence  of  electric  force 
inside  a  closed  conductor ;  this  fact  enables  us  to  de- 
monstrate the  necessary  truth  of  the  "law  of  inverse 
squares  "  which  was  first  experimentally,  though  roughly, 
proved  by  Coulomb  with  the  torsion  balance.     Suppose 
a  point  P  anywhere  inside  a  hollow  sphere  charged  with 
electricity  (Fig.  98).     The  charge  is  uniform  all  over, 
and  the  quantity  of  electricity 
on    any   small    portion  of  its 
surface    will    be    proportional 
to  the  area  of  that  portion. 
Consider    a    small   portion  of 
the  surface  AB.     The  charge 
on  AB  would  repel  a  +  unit 
placed    at    P  with   a   certain 
force.      Now  draw   the    lines 
AD  and  BC  through  P,  and 
regard  these  as  mapping  out 
a   small    conical    surface    of 
two  sheets,  having  its  apex  at  P ;  the  small  area  CD 
will  represent  the  end  of  the  opposed  cone,    and  the 
electricity  on  CD  will  also  act  on  the  +  unit  placed  at  P, 
and  repel  it.     Now  these  surfaces  AB  and  CD,  and  the 
charges  on  them,  will  be  directly  proportional  to  the 
squares  of  their  respective  distances  from  P.     If,  then 


Fig.  98. 


202  ELEMENTARY  LESSONS  ON       [CHAP,  iv 

the  forces  which  they  exercise  on  P  exactly  neutralise 
one  another  (as  experiment  shows  they  do),  it  is  clear 
that  the  electric  force  must  fall  off  inversely  as  the 
squares  of  the  distances;  for  the  whole  surface  of  the 
sphere  can  be  mapped  out  similarly  by  imaginary  cones 
drawn  through  P.  The  reasoning  can  be  extended  also 
to  hollow  conductors  of  any  form. 

246.  Capacity. — In    Lesson   IV.   tne    student    was 
given   some   elementary  notions   on  the  subject  of  the 
Capacity   of  conductors.     We   are  now    ready  to   give 
the  precise  definition.     The  Electrostatic  Capacity  of 
a  .conductor   is  measured  by  the  quantity  of  electricity 
which  must  be  imparted  to  it  in  order  to  raise  its  potential 
from  zero  tv  unity.     A   small   conductor,    such   as   an 
insulated  sphere  of  the  size  of  a  pea,  will  not  want  so 
much  as   one   unit   of  electricity  to   raise   its   potential 
from  o  to  i  ;   it  is  therefore  of  small  capacity — while 
a  large  sphere  will  require  a  large  quantity  to  raise  its 
potential  to  the  same  degree,  and  would   therefore   be 
said  to  be  of  large  capacity.      If  C  stand    for  capacity, 
and  Q  for  a  quantity  of  electricity, 

C  =  •§      and      C  V  =  Q. 

This  is  equivalent  to  saying  in  words  that  the  quantity 
of  electricity  necessary  to  charge  a  given  conductor  to 
a  given  potential,'  is  numerically  equal  to  the  product  of 
the  capacity  into  the  potential  through  which  it  is  raised. 

247.  Unit  of  Capacity. — A  conductor  that  required 
only  one  unit  of  electricity  to  raise  its  potential  from  o 
to  I,  would  be^said  to  possess  unit  capacity.     A  sphere 
one  centimetre  in  radius*  possesses  unit   capacity ;  for 
if  it  be  charged  with  a  quantity  of  one  unit,  this  charge 
will  act  as   if  it  were*"coflected   at   its  centre.     At  the 
surface,  which  is  one  centime; re  away  from  the  centre, 

the  potential,  which  is  measured  as  ^,  will  be  i.  Hence, 
as  I  unit  of  quantity  raises  it  to  unit  i  of  potential,  the 


CHAP,  iv.]  ELECTRICITY  AND  MAGNETISM.  203 

sphere  possesses  unit  capacity.  The  capacities  of  spheres 
are  "Proportional  to  their  radii.  Thus,  a  sphere  of  one 
metre  radius  has  a  capacity  of  IOQ,  The  earth  has  a 
capacity  of  about  630  millions  (jn  electrostatic  units). 
It  is  "almost  impossible  to'  calculate  the  capacities  of 
conductors  of  other  shapes.  It  must  be  noted  that  the 
capacity  of  a  sphere,  as1  given  above,  means  its  capacity 
when  far  removed  from  other  conductors  or  charges  of 
electricity.  The  capacity  of  a  conductor  is  increased  by. 
bringing  near  it  a  charge  of  an  opposite  kind ;  for  the 
potential  at  the  surface  of  the  conductor  is  the  sum  of 
the  potential  due  to  its  own  charge,  and  of  the  potential 
of  opposite  sign  due  to  the  neighbouring  charge.  Hence, 
to. bring  up  the  resultant  potential  to  unity,  a  larger 
quantity  of  electricity  must  be  given  to  it;  or,  in  other 
words,  its  capacity  is  greater.  This  is  the  true  way  of 
regarding  the  action  of  Ley  den  jars  and  other  accumu- 
lators, and  must  be  remembered  by  the  student  when  he 
advances  to  the  consideration  of  the  theory  of  accumu- 
lators, in  Lesson  XXII. 

248.  Surface-density.1 — Coulomb  applied  this  term 
to  denote  the  amount  of  electricity  per  unit  of  area  at  any 
point  of  a  surface.  It  was  mentioned  in  Lesson  IV.  that 
a  charge  of  electricity  was  never  distributed  uniformly 
byer  a  conductor,  except  in  the  case  6f  an  insulated 
sphere.  Where  the  distribution  is  unequal,  the  density 
at  any  point  of  the  surface  may  be  expressed  by  con- 
sidering the  quantity  of  electricity  which  exists  upon  a 
small  unit  of  area  at  that  point.  If  Q  be  the  quantity 
of  electricity  on  the  small  surface,  and  S  be  the  area  ol 

1  The  word  Tension  is  sometimes  used  for  that  which  is  here  precisely 
defined  as  Coulomb  defined  it.  The  term  tension  is,  however,  unfortunate  ; 
and  it  is  so  often  misapplied  in  text-books  to  mean  not  only  surface-density 
but  also  potential,  and  even  electric  force  (i.e.,'ihe  mechanical  force  exerted 
upon  a  material  body  by  electricity),  that  we  avoid  its  use  altogether.  The 
term  would  be  invaluable  if  we  might  adopt  it  to  denote  only  the  mechanical 
stress  across  a  dielectric,  due  to  accumulated  charges ;  but  so  long  as  the 
above  confusion  lasts,  it  is  better  to  drop  Ihe  term  entirely,  and  the  student 
will  have  one  thing  fewer  tp  learn  -and  to  unlearn. 


204  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

that  small  surface,  then  the  surface  density  (denoted  by 
the  Greek  letter  p)  will  be  given  by  the  equation, 


In  dry  air,  the  limit  to  the  possible  electrification  is 
reached  when  the  density  reaches  the  value  of  about  20 
units  of  electricity  per  square  centimetre.  If  charged  to 
a  higher  degree  than  this,  the  electricity  escapes  in 
"  sparks  "  and  "  brushes  "  into  the  air  In  the  case  of 
uniform  distribution  over  a  surface  (as  with  the  sphere, 
and  as  approximately  obtained  on  a  flat  disc  by  a  parti- 
cular device  known  as  a  guard-ring),  the  density  is  found 
by  dividing  the  whole  quantity  of  the  charge  by  the 
whole  surface. 

249  Surface-Density  on  a  Sphere.  —  The  surface 
of  a  sphere  whose  radius  is  r,  is  4?rr2.  Hence,  if  a 
charge  Q  be  imparted  to  a  sphere  of  radius  r,  the  surface- 

density  all  over  will  be  p  =  —  -^-;  or,  if  we  know  the 

surface  -  density,    the   quantity   of    the   charge    will    be 
Q  =•  47rr2/). 

The  surface-density  on  two  spheres  joined  by  a  thin 
wire  is  an  important  case.  If  the  spheres  are  unequal, 
they  will  share  the  charge  in  proportion  to  their  capacities 
(see  Art.  37),  that  is,  in  proportion  to  their  radii.  If  the 
spheres  are  of  radii  2  and  i,  the  ratio  of  their  charges 
-will  also  be  as  2  to  i.  But  their  respective  densities  will 
be  found  by  dividing  the  quantities  of  electricity  on  each 
by  their  respective  surfaces.  But  the  surfaces  are  pro- 
portional to  the  squares  of  the  radii,  i.e.,  as  4  :  r  ;  hence, 
the  densities  will  be  as  i  :  2,  or  inversely  as  the  radii. 
Now,  if  one  of  these  spheres  be  very  small  —  no  bigger 
than  a  point  —  the  density  on  it  will  be  relatively 
immensely  great,  so  great  that  the  air  particles  in  con- 
tact with  it  will  rapidly  carry  off  the  charge  by  convection. 
This  explains  the  action  of  points  in  discharging  con- 
ductors, noticed  in  Chapter  I.  Arts.  35  c%  42  and  43. 


CHAP.  IV.]    ELECTRICITY  AND  -MAGNETISM.  205 

25O.  Electric  linages. — It  can  be  shown  mathe- 
matically that  if  +  q  units  of  electricity  are  placed  at  a 
point  near  a  non-electrified  conducting  sphere  of  radius 
r,  at  a  distance  d  from  its  centre,  the  negative  induced 

charge  will  be  equal  to  —  -,q,  and  will  be  distributed  over 

the  nearest  part  of  the  surface  of  the  sphere  with  a 
surface-density  inversely  proportional  to  the  cube  of  the 
distance  from  that  point.  Sir  W.  Thomson  pointed  out 
that,  So  far  as  all  external  points  are  conceined,  the 
potential  due  to  this  peculiar  distribution  on  the  suiface 
would  be  exactly  the  same  as  if  this  negative  charge  were 

all  collected  at  an  internal  point  at  a  distance  of  r  —  j 
behind  the  surface.  Such  a  point  may  be  regarded  as  a 
virtual  image  of  the  external  point,  in  the  same  way  as  in 
optics  we  regard  certain  points  behind  mirrors  as  the 
virtual  images  of  the  external  points  from  which  the  rays 
proceed.  Clerk  Maxwell  has  given  the  following  defini- 
tion of  an  Electric  Image  : — An  electric  image  is  an 
electrified  point)  or  system  of  point s^  on  one  side  of  a  surf  ace  ^ 
which  would  produce  on  the  other  side  of  that  surface  the 
same  electrical  action  which  the  actual  elecirijication  oj 
that  surface  really  does  produce.  A  charge  of  +  elec- 
tricity placed  one  inch  from  a  flat  metallic  plate  induces 
on  it  a  negative  charge  distributed  over  the  neighbouring 
region  of  the  plate  (with  a  density  varying  -inversely  as 
the  cube  of  the  distance  from  the  point) ;  but  the 
electrical  action  of  this  distribution  would  be  precisely 
represented  by  its  "  image,"  namely,  by  an  equal  quantity 
of  negative  electricity  placed  at  a  point  one  inch  behind 
the  plate.  Many  beautiful  mathematical  applications  of 
this  method  have  been  made,  enabling  the  distribution 
to  be  calculated  in  difficult  cases,  as,  for  example,  the 
distribution  of  the  charge  on  the  inner  surface  of  a  hollow 
bowl. 

251,  Electric    Force    exerted    by    a    Charged 


2o6  ELEMENTARY  LESSONS  ON      [CHAP.  iv. 

Sphere  at  a  point  near  to  it. — It  was  shown 
above  that  the  quantity  of  electricity  Q  upon  a  sphere 
charged  until  its  surface-density  was  /o,  was 

Q  =  4  Trr*p. 

The  problem  is  to  find  the  force  exercised  by  this 
charge  upon  a  +  unit  of  electricity,  placed  at  a  point 
infinitely  near  the  surface  of  the  sphere.  The  charge  on 
the  sphere  acts  as  if  at  its  centre.  The  distance  between 
the  two  quantities  is  therefore  r.  By  Coulomb's  law  the 
force/ =  °^J  =  4^fP  =4vpt 

This  important  result  may  be  stated  in  words  as 
follows  : — The  force  (in  dynes)  exerted  by  -a  charged 
sphere  upon  a  unit  of  electricity  placed  infinitely  near  to 
Us  surface,  is  numerically  equal  to  477  times  the  surface- 
density  of  the  charge. 

252.  Electric   Force    exerted    by  a    charged 
plate  of  indefinite  extent  on  a  point  near  it.— 
Suppose  a  plate  of  indefinite  extent  to  be  charged  so  that 
it  has  a  surface-density  p.     This  surface-density  will  be 
uniform,  for  the  edges  of  the  plate  are  supposed  to  be 
so  far  off  as  to  exercise  no  influence.      It  can  be  shown 
that  the  force  exerted  by  such  a  plate  upon  a  +  unit  any- 
where near  it,  will  be  expressed  (in  dynes)  numerically 
as  2irp.    This  will  be  of  opposite  signs  on  opposite  sides 
of  the  plate,  being  +  27173  on  one  side,  and  -  27173  on  the 
other  side,  since  in  one  case  the  force  tends  to  move  the 
unit  from  right  to  left,  in  the  other  from  left  to  right 
It  is  to  be  observed,  therefore,  that  the  force  changes  its 
value  by  the  amount  of  477/3  as  the  point  passes  through 
the  surface.     The  same  was  true  of  the  charged  sphere, 
where  the  force  outside  was  477/0,  and  inside  was  zero. 
The  same  is  true  of  all  charged  surfaces.     These  two 
propositions  are  of  the  utmost  importance  in  the  theory 
of  Electrostatics. 

253.  The  elementary  geometrical  proof  of  the  latter  theorem 
is  as  follows  : — 


CHAP,  iv.]  ELECTRICITY  AND  MAGNETISM. 


207 


Required  the  Electric  Force  at  point  at  any  distance  from  a 
plane  of  infinite  extent  cnarged  to  surface-density  p. 

Let  P  be  the  point, 
and  PX  or  a  the  normal 
to  the  plane.  Take  any 
small  cone  having  its 
apex  at  P.  Let  the 
solid-angle  of  this  cone 
be  V,  let  its  length  be 
r;  and  0  the  angle  its 
axis  makes  with  a.  The 
cone  meets  the  surface 
of  the  plane  obliquely, 
and  if  an  orthogonal 
section  be  made  where 
it  meets  the  plane,  the 
angle  between  these  sections  will  be  =  0. 

.,                              .    ,      ,  -  .. .           orthogonal  area  of  section 
Now  solid-angle  w  is  by  definition  = 3 

Hence,    area   of  oblique   section  =  r'a  x 


Fig.  99. 


charge    on    oblique    section  =  ^ 


cos  6 


cos  9 


Hence  if  a  +  unit  of  electricity  were   placed  at  P,  the  force 

exerted  on  this  by  this  small  charge  =  •?-—.  x 

cos  9 

up 
or  = 


I  -f- 


cos  9 

Resolve  this  force  inter  two  parts,  one  acting  along  the  plane, 
the  other  along  a,  normal  to  the  plane.  The  normal  component 

along  a  is  cos  9  x  — ^  =  up 
cos  v 

But  the  whole  surface  of  the  plane  may  be  similarly  mapped 
out  into  small  surfaces,  all  forming  small  cones,  with  their  summits 
at  P.  If  we  take  an  infinite  number  of  such  small  cones  meeting 
every  part,  and  resolve  their  forces  in  a  similar  way,  we  shall 
find  that  the  components  along  the  plane  will  neutralise  one. 
another  all  round,  while  the  normal  components,  or  the  resolved 
forces  along  a,  will  be  equal  to  the  sum  of  all  their  solid -angles 
multiplied  by  the  surface-density  ;  or 

Total  resultant  force  along  a  • 


2o8  ELEMENTARY  LESSORS  Oil       [CI:AP.  rv 

But  the  total  solid-angle  subtended  by  an  infinite  plane  at  a 
point  is  2r,  for  it  subtends  a  whole  hemisphere. 

.*.  Total  resultant  force  =  2vp. 


NOTE  ON  FUNDAMENTAL  AND  DERIVED   UNITS. 

254.  Fundamental  Units. — All  physical  quantities,  such  g.s 
force,   velocity,  etc.,  can  be  expressed  in   terms  of  the  threa 
fundamental  quantities  :  length^  mass,  and  time.     Each  of  thesa 
quantities  must  be  measured  in  terms  of  its  own  units. 

The  system  of  units,  adopted  by  almost  universal  consent, 
and  used  throughout  these  Lessons,  is  the  so-called  "  Centi- 
metre -  Gramme  •  Second "  system,  in  which  the  fundamental 
units  £T3  : — 

The  Centimetre  as  a  unit  of  length  ; 

The  Gramme  as  a  unit  of  mass  ; 

The  Second  as  a  unit  of  time. 

The  Centimetre  is  equal  to  0*3937  inch  in  length,  and  no- 
minally represents  one  thousand -millionth  part,  or  j^ooTo^D.Too 
of  a  quadrant  of  the  earth. 

The  Metre  is  100  centimetres,  or  39*37  inches. 

The  Kilometre  is  1000  metres,  or  about  1093*6  yards. 

The  Millimetre  b  the  tenth  part  of  a  centimetre,  or  0*03937 
inch. 

The  Gramms  is  equal  to  15*432  grains,  and  represents  the 
mass  of  a  cubic  centimetre  of  water  at  4°  C  :  the  Kilogranitns  is 
IOQO  grammes  or  2*2  pounds. 

255.  Derived  Units. — 

Area. — The  unit  of  area  is  the  square  centimetre. 

Volume. — The  unit  of  volume  is  the  cubic  centimetre. 

Velocity. — The  unit  of  velocity  is  the  velocity  of  a  bou) 
which  moves  through  unit  distance  in  unit  tune,  or  the 
velocity  of  one  centimetre  per  second. 

Acceleration. — The  unit  of  acceleration  is  that  acceleration 
which  imparts  unit  velocity  to  a  body  in  unit  time,  or 
an  acceleration  of  one  centimetre-per -second  per  second. 
The  acceleration  clue  to  gravity  imparts  in  one  second 
a  velocity  considerably  greater  than  this,  for  the  velocity 
it  imparts  to  falling  bodies  is  about  981  centimetres  per 


JHAP.  iv.]    ELECTRICITY  AND  MAGNETISM.  209 


second  (or  about  32*2  feet  per  second).  The  value  differs 
slightly  in  different  latitudes.  At  Bristol  the  value  of 
the  acceleration  of  gravity  is  g  —  981*1 ;  at  the  Equator 
g  =  975-1 ;  at  the  North  Pole  g  =  983'!. 

Force.  The  unit  of  fores  is  that  force  which,  acting  for  one 
second  on  a  mass  of  one  gramme,  gives  to  it  a  velocity 
of  one  centimetre  per  second.  It  is  called  one  Dyne. 
The  force  with  which  the  earth  attracts  any  mass  is 
usually  called  the  "  weight "  of  that  mass,  and  its  value 
obviou-'-y  differs  at  different  points  of  the  earth's  surface. 
The  fnrce  with  wliich  a  body  gravitates,  i.e.  its  weight 
(in  dynes),  is  found  by  multiplying  its  mass  (hi  grammes) 
by  the  A  alue  of  g  at  the  particular  place  where  the  force 
is  exerted. 

}Vorh. — The  unit  of  v/ork  is  the  work  done  hi  overcoming 
unit  force  through  unit  distance,  i.e.  in  pushing  a  body 
through  a  distance  of  one  centimetre  against  a  force  of 
one  dyne.  It  is  called  one  Erg.  Since  the  "weight" 
of  one  gramme  is  I  x  981  or  981  dynes,  the  work  ol 
raising  one  gramme  through  the  height  of  one  centimetre 
against  the  force  of  gravity  is  98 1  ergs. 

Energy.  — The  unit  of  energy  is  also  the  erg  ;  for  the  energy 
of  a  body  is  measured  by  the  work  it  can  do. 

Heat. — The  unit  of  heat  (sometimes  called  a  calorie}  is  the 
amount  of  heat  required  to  warm  one  gramme  mass  of 
water  fiom  o°  to  1°  (C);  and  the  dynamical  equivalent 
of  this  amount  of  heat  is  42  million  ergst  which  is  the 
value  of  Joule's  equivalent,  as  expressed  in  absolute 
(C.G.S.)  measure.  (See  also  Art  367.) 

Tliese  units  are  sometimes  called  "  absolute  "  units  ;  the  term  absolute, 
introduced  by  Gauss,  meaning  that  they  are  independent;  of  the  size  of  any 
particular  instrument,  or  of  the  value  of  gravity  at  any  particular  place,  or  of 
any  other  arbitrary  quantities  than  the  three  standards  of  length,  mass,  and 
time.  It  is,  however,  preferable  to  refer  to  them  by  the  more  appropriate 
name  of  "  CG.S.  units,"  as  being  derived  from  the  centimetre,  the  gramme, 
and  the  second. 

256.  Electrical  Units. — There  are  two  systems  of  electrical 
units  derived  from  the  fundamental  "C.G.  S."  units,  one  set 
being  based  upon  the  force  exerted  between  two  quantities  of 
electricity,  and  the  other  upon  the  force  exerted  between  two 
magnet  poles.  The  former  set  are  termed  electrostatic  units,  the 
latter  electromagnetic  units.  The  important  relation  between  the 
two  sets  is  explained  in  the  note  at  the  end  of  Lesson  XXX. 

P 


aio  ELEMENTARY  LESSONS  ON      [CHAP.  iv. 

257.  Electrostatic  Units. — No    special   names   have  been 
assigned   to   the    electrostatic    units    of    Quantity,    Potential, 
Capacity,  etc.     The  reasons  for  adopting  the  following  values 
as  units  are  given  either  in  Chapter  I.  or  in  the  present  Chapter. 

Unit  of  Quantity. — The  unit  of  quantity  is  that  quantity  of 
electricity  which,  when  placed  at  a  distance  of  one 
centimetre  (in  air)  from  a  similar  and  equal  quantity, 
repels  it  with  a  force  of  one  dyne  (Art.  236). 

Potential. — Potential  being  measured  by  work  done  in  moving 
a  unit  of  +  electricity  against  the  electric  forces,  the  unit 
of  potential  will  be  measured  by  the  unit  of  work,  the  erg. 

Unit  Difference  of  Potential. — Unit  difference  of  potential 
exists  between  two  points,  when  it  requires  the  expendi- 
ture of  one  erg  of  work  to  bring  a  unit  of  +  electricity 
from  one  point  to  the  other  against  the  electric  force 
(Art.  242). 

Unit  of  Capacity. — That  conductor  possesses  unit  capacity 
which  requires  a  charge  of  one  unit  of  electricity  to  bring 
it  up  to  unit  potential.  A  sphere  of  one  centimetre 
radius  possesses  unit  capacity  (Art.  247). 

Specific  Inductive  Capacity  is  defined  in  Art.  268  as  the  ratio 
between  two  quantities  of  electricity.  The  specific- 
inductive  capacity  of  the  air  is  taken  as  unity. 

258.  Dimensions  of  Units. — It  has  been  assumed   above 
that  a  A  elocity  can  be  expressed  in  centimetres  per  second  ;  for 
velocity  is  rate  of  change  of  place,  and  it  is  clear  that  if*  change 
of  place  may  be  measured  as  a  length  in  centimetres,  the  rate 
of  change  of  place  will  be  measuied  by  the  number  of  centit 
metres  through  which  the"  body  moves  in  unit   of  time.     It  is 
impossible,  indeed,  to  express  a  velocity  without  regarding  it  as 
the  quotient  of  a  certain  number  of  units  of  length  divided  by 
a  certain  number  of  units  of  time.     In  other  words,  a  velocity 

=  &a  ^~e-  J  or,  adopting  L  as  a  symbol  for  length,  and  T  as  a 
symbol  for  time,  V  =  ^,  which  is  still  more  conveniently  written 

V  =  L  x  T  ~  .     hi  i  similar   way  acceleration  being  rate  of 
change  of  velocity,  we  have  A  =  ^  =  ^~  =  ^  =  L  x  T  ~  • 

Now  these  physical  quantities,  "velocity,"  and  "acceleration," 
are  respectively  always  quantities  of  the  same  nature,  no  mailer 
whether  the  centimetre,  or  the  inch,  or  the  mile,  be  taken  as  the 
unit  of  length,  or  the  second  or  any  other  interval  be  taken  as 


CHAP,  iv.l    ELECTRICITY  AND  MAGNETISM. 


211 


the  unit  of  time.  Hence  we  say  that  these  abstract  equations 
express  the  "dimensions"  of  those  quantities  with  respect  to  the 
fundamental  quantities  length  and  time.  A  little  consideration 
will  show  the  student  that  the  following  will  therefore  be  the 
dimensions  of  the  various  units  mentioned  above  : — 


UNITS. 

DIMENSIONS. 

(Fundamental.  )    • 

L 

M 
T 

m 
t 

Length 
Mass 
Time 

(Derived.) 

Area 

L   x    L                     = 

L8 

Volume 

=         L   x   L  x  L             SB 

L8 

V 

Velocity 

L  ^  T 

LT"1 

a, 
f 

Acceleration 
Force 

=   velocity  -T-  time             = 
=   mass    x    acceleration     = 

MLT" 

i 

Work 

=   force'  x    length              = 

ML'T' 

f 

(Electrostatic.) 
Quantity 

L 

a  numeral 

M2  L^  T~ 

=    Vforce  X  (distance)  3  = 

i 

Current 

=   quantity  -J-  time    = 

V 

Potential 

—   work  -T-  quantity  = 

R 
C 

k 

Resistance               =  -potential  -f-  current    = 
Capacity                  =   quantity  ~  potential  = 
Sp.  Ind.  Capacity  =  quantity  -j-  another  quantity 

Electromotive 

Intensity  =  force  -r-  quantity  = 

The  dimensions  of  magnetic  units  are  given  in  the  note  on 
Magnetic  Units,  Art.  324. 

LESSON  XXI. — Electrometers. 

259.    In  Lesson  II.  we  described  a  number  of  electro- 
scopes or  instruments   for  indicating  the  presence   and 


212  ELEMENTARY  LESSONS  ON       [CHAP,  iv 

sign  of  a  charge  of  electricity  ;  some  of  these  also  served 
to  indicate  roughly  the  amount  of  these  charges,  but  none 
of  them  save  the  -torsion  balance  could  be  regarded  as 
affording  an  accurate  means  of  measuring  either  the 
quantity  or  "Chz  potential  of  a  given  charge.  An  instru- 
ment for  measuring-  differences  of  electrostatic  potential  is 
termed  an  Electrometer.  Such  instruments,  can  also 
be  used  to  measure  electric  quantity  indirectly,  for  the 
quantity  of  a  charge  can  be  ascertained  by  measuring 
the  potential  to  which  it  can  raise  a  conductor  of  known 
capacity.  The  earliest  electrometers  attempted  to  measure 
the  quantities  directly.  Lane  and  Snow  Harris  constructed 
"  Unit  Jars  "  or  small  Leyden  jars,  which,  when  it  was 
desired  to  measure  out  a  certain  quantity  of  electricity, 
were  charged  and  discharged  a  certain  number  of  times. 
The  discharging  gold-leaf  electroscope  of  Gaugain  was 
invented  with  a  similar  idea. 

26O.  Repulsion  Electrometers.  —  The  torsion 
balance,  described  in  Art.  1 5,  measures  quantities  by 
measuring  the  forces  exerted  by  the  charges  given  to  the 
fixed  and  movable  balls.  It  can  only  be  applied  to  the 
measurement  of  repelling  forces,  for  the  equilibrium  is 
unstable  in  the  case  of  a  force  of  attraction. 

There  are,  besides  the  gold-leaf  electroscope  and  the 
Lane's  electroscope,  described  in  Lesson -I I.,  a  number 
of  finer  electrometers  based  upon  the  principle  of  repul- 
sion, some  of  which  resemble  the  torsion  balance  in 
having  a  movable  arm  turning  about  a  central  axis. 
Amongst  these  are  the  electrometers  of  Dellmann  and  of 
Peltier  ;  the  latter  of  these  is  shown  in  Fig.  1 1 1,  in  the 
Lesson  on  Atmospheric  Electricity.  In  this  apparatus  a 
light  arm  of  aluminium,  balanced  upon  a  point,  carries 
also  a  smafl  magnet  to  direct  it  in  the  magnetic  meridian. 
A  fixed  arm,  in  metallic  contact  with  the  movable  one, 
also  lies  in  the  magnetic  meridian.  A  charge  imparted 
to  this  instrument  produces  a  repulsion  between  the  fixed 
and  movable  arms,  causing  an  angular  deviation.  Here, 


CHAP,  iv.j   ELECTRICITY  AND  MAGNETISM.         '    213 

hov/ever,  the  force  is  measured  not  by  being  pitted  against 
the  torsion  of  an  elastic  fibre,  or  against  gravitation,  but 
against  the  directive  magnetic  force  of  the  earth  acting 
on  the  small  needle.  Now  this  depends  on  the  intensity 
of  the  horizontal  component  of  the  earth's  magnetism  at 
the  place,  on  the  magnetic  moment  of  the  needle,  and 
on  the  sine  of  the  angle  of  its  deviation.  Moreover,  the 
repulsion  here  is  not  between  two  charges  collected  on 
small  spheres,  but  between  the  fixed  arm  and  the  mov- 
able one.  Hence,  to  obtain  quantitative  values  for  the 
readings  of  this  electrometer,  it  is  necessary  to  make 
preliminary  experiments  and  to  "  calibrate  "  the  degree- 
readings  of  the  angular  deviation  to  an  exact  scale. 

261.  Attracted  -  Disc  Electrometers.  —  Snow 
Harris  was  the  first  to  construct  an  electrometer  for 
measuring  the  attraction  between  an  electrified  and  a 
non-electrified  disc ;  and  the  instrument  he  devised  may 
be  roughly  described  as  a  balance  for  weighing  a  charge 
of  electricity.  More  accurately  speaking,  it  was  an 
instrument  resembling  a  balance  in  form,  carrying  at  one 
end  a  light  scale  pan ;  at  the  other  a  disc  was  hung 
above  a  fixed  insulated  disc,  to  which  the  charge  to  be 
measured  was  imparted.  The  disadvantages  of  this 
instrument  were  manifold,  the  chief  objection  being  due 
to  the  irregular  distribution  of  the  charge  on  the  disc. 
The  force  exerted  by  an  electrified  point  falls  off  inversely 
as  the  square  of  the  distance,  since  the  lines  of  force 
emanate  in  radial  lines.  But  in  the  case  of  a  uniformly 
electrified  plane  surface,  the  lines  of  force  are  normal  to 
the  surface,  and  parallel  to  one  another ;  and  the  force 
is  independent  of  the  distance.  The  distribution  over 
a  small  sphere  nearly  fulfils  the  first  of  these  conditions. 
The  distribution  over  a  flat  disc  would  nearly  fulfil  the 
latter  condition,  were  it  not  for  the  perturbing  effect  of 
the  edges  of  the  disc  where  the  surface-density  is  much 
greater  (see  Art.  35);  for  this  reason  Snow  Harris's 
electrometer  was  very  imperfect 


214 


ELEMENTARY  LESSONS  ON       [CHAP.  iv. 


Sir  W.  Thomson  has  introduced  several  very  import- 
ant modifications  into  the  construction  of  attracted-disc 
electrometers,  the  chief 'of  these  being  the  employment 
of  the  "  guard-plate "  and  the  providing  of  means  for 
working  with  a  definite  standard  of  potential.  It  would 
be  beyond  the  scope  of  these  lessons  to  give  a  complete 
description  of  all  the  various  forms  of  attracted-disc 
electrometer ;  but  the  main  principles  of  them  all  can  be 
readily  explained. 

The  disc.  C,  whose  attraction  is  to  be  measured,  is  sus- 
pended (Fig.  100)  within  a  fixed  guard-plate,  B,  which 


surrounds  it  without  touching  it,  and  which  is  placed 
in  metallic  contact  with  it  by  a  fine  wire.  A  lever,  L, 
supports  the  disc,  and  is  furnished  with  a  counterpoise  ; 
whilst  the  aluminium  wire  which  serves  as  a  fulcrum  may 
be  also  employed  to  produce  a  torsion  force.  In  order 
to  know  whether  the  *disc  is  precisely  level  with  the 
lower  surface  of  the  guard-plate  a  little  gauge  or  index 
is  fixed  above,  and  provided  with  a  lens,  /,  to  observe 
its  .indications,  Beneath  the  disc  and  guard-plate  is 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM.  215 

a  second  disc,  A,  supported  on  an  insulating  stand.  This 
lower  disc  can  be  raised  or  lowered  at  will  by  a  micro- 
meter screw,  great  care  being  taken  in  the  mechanical 
arrangements  that  it  shall  always  be  parallel  to  the 
plane  of  the  guard  -plate.  Now,  since  the  disc  and 
guard-plate  are  in  metallic  connection  with  one  another, 
they  form  virtually  part  of  one  surface,  and  as  the 
irregularities  of  distribution  occur  at  the  edges  of  the 
surface,  the  distribution  over  the  surface  of  the  disc  is 
practically  uniform.  Any  attraction  of  the  lower  plate 
upon  the  disc  might  be  balanced  either  by  increasing 
the  weight  of  the  counterpoise,  or  by  putting  a  torsion 
on  the  wire  ;  but  in  practice  it  is  found  most  convenient 
ito  obtain  a  balance  by  altering  the  distance  of  the  lower 
^ate  until  the  electric  force  of  attraction  exactly 
oalances  the  forces  (whether  of  torsion  or  of  gravity 
acting  on  the  counterpoise)  which  tend  to  lift  the  disc 
above  the  level  of  the  guard-plate. 

The  theory  of  the  instrument  is  simple  also.  The 
force  F  just  outside  a  charged  conducter  is  47:73  (Art. 
252);  and  since  electric  force  is  the  same  thing  as 
the  rate  of  change  of  potential  per  unit  of  length 
(Art.  241),  it  will  be  equal  to  g,  where  V  is  the 

difference   of  potentials  between  the  upper   and  lower 

V 
plates,  and  D  the  distance  between  them  :  hence  p  = 


If  the  surface  of  the  movable  disc  be  S,  the  quantity  of 
the  charge  on  it  will  be  Sp.  Now,  let  us  suppose  that 
the  electricity  on  the  lower  plate  has  an  equal  density 
but  of  opposite  sign,  as  will  be  the  case  if  either  plate  is 
connected  to  "earth."  Since  its  density  is  —  p  it  will 
exercise  a  force  of  —  nrp  on  a  +  unit  placed  near  the  disc; 
(but  as  this  force  is  a  force  exerted  from  the  upper  side 
of  the  plate  we  must  change  its  sign  again  and  call  it 
+  27T/3,  where  the  +  sign  signifies  a  force  tending  to 
move  a  +  unit  downwards.)  Now  on  the  disc  there  au-e 


216  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

Sp  units  of  e.ectricity  ;  hence  the  total  force  of  attraction 
on  the  disc  will  be  F  =  27173  x  Sp. 


V2 

7 
S     V2 


whence  V  =  ^     ' 8?rF 


From  this  we  gather  that,  if  the  force  F  remain  the 
same  throughout  the  experiments,  the  difference  of  po- 
tentials between  the  discs  will  be  simply  proportional  to 
the  distance  between  them  when  the  disc  is  in.  level 


I  Q      Tp 

equilibrium.      And  the  quantity  ./  -^-  may  be  deter- 

mined once  for  all  as  a  "constant"  of  the  instrument. 

In  the  more  elaborate  forms  of  the  instrument,  such 
as  the  "  absolute  electrometer,"  and  the  "  portable 
electrometer,"  the  disc  and  guard  -plate  are  covered 
with  a.  metallic  cage,  and  are  together  placed  in  com- 
munication with  a  condenser  to  keep  them  at  a  known 
potential.  This  obviates  having  to  make  measurements 
with  zero  readings,  for  the  differences  of  potential  will 
now  be  proportional  to  differences  of  micrometer  readings  •, 

or,  V.-V^XD.-D,) 


The  condenser  is  provided  in  these  instruments  with 
a  gauge,  itself  an  attracted-disc;  to  indicate  when  it  is 
charged  to  the  right  potential,  and  with  a  replenisher  to 
increase  or  decrease  the  charge,  the  replenisher  being 
a  little  convection-induction  machine  (see  Art.  4  5). 

262.  The  Quadrant  Electrometer.  —  The  Quad- 
rant  Electrometer  of  Sir  W.  Thomson  is  an  example  oi 
a  different  class  of  electrometers,  in  which  use  .  is  made 
of  an  auxiliary  charge  of  electricity  previously  imparted 
to  the  needle  of  the  instrument.  The  needle,  which  con- 


riiAP.  iv.]   ELECTRICITY  AND  MAGNETISM. 


sists  of  a  thin  flat  piece  of  metal  hung  horizontally  by  a 
fibre  or  thin  wire,  thus  charged  with,  say,  +  electricity, 
will  be  attracted  by  a  —  charge,  but  repelled  by  a  + 
charge ;  and  such  attraction  or  repulsion  will  be  stronger 
in  proportion  to  these  charges,  and  in  proportion  to  the 
charge  on  the  needle.  Four  quadrant -pieces  of  brass 
are  fixed  horizontally  below  the.  needle  without  touching 
it  or  one  another.  Opposite  auadrants  are  joined  with 
fine  wires. 

Fig.  101  shows  a  very  simple  form  of  the  Ouadram 
Electrometer,  as   arranged   for   qualitative  experiments. 


Fig.  101. 


The  four  quadrants  are  enclosed  within  a  glass  case,  and 
the  needle,  which  carries  a  light  mirror,  M,  below  ^it,  is 
suspended  from  a  torsion,  head,  C,  by  a  very  thin  metallic 
wire,  F.  It  is  electrified  to  a  certain  potential  by  being 
connected,  through  a  wire  attached  to  C,  with  a  charged 


2i8  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

Leyden  jar  or  other  condenser.  In  order  to  observe 
the  minutest  motions  of  the  needle,  a  reading-telescope 
and  scale  are  so  placed  that  the  observer  looking  through 
the  telescope  sees  an  image  of  the  zero  of  the  scale 
reflected  in  the  little  mirror.  The  wires  connecting 
quadrants  I  and  3,  2  and  4,  are  seen  above  the  top  of 
the  case.  The  needle  and  quadrants  are  shown  in  plan 
separately  above.  Jf  there  is  the  slightest  difference  of 
potential  between  the  pairs  of  quadrants,  the  needle, 
which  is  held  in  its  zero  position  by  the  elasticity  of  the 
wire,  will  turn,  and  so  indicate  the  difference  of  potential. 
When  these  deflections  are  small,  the  scale  readings  will 
be  very  nearly  proportional  to  the  difference  of  potential. 
The  instrument  is  sufficiently  delicate  to  show  a  difference 
of  potential  between  the  quadrants  as  small  as  the  ^  of 
that  of  the  Daniell's  cell. 

For  very  exact  measurements  many  additional  refine- 
ments are  introduced  into  the  instrument.  Two  sets  of 
quadrants  are  employed,  an  upper  and  a  lower,  having 
the  needle  between  them.  The  torsion  wire  is  replaced 
by  a  delicate  bifilar  suspension  (Art.  118).  To  keep 
up  the  charge  of  the  Leyden  jar  a  "  Replenisber  "  is 
added  ;  and  an  "  attracted-disc,"  like  that  of  the  Absolute 
Electrometer,  is  employed  in  order  to  act  as  a  gauge  to 
indicate  when  the  jar  is  charged  to  the  right  potential. 
In  these  forms  the  jar  consists  of  a  glass  vessel  placed 
below  the  quadrants,  coated  externally  with  strips  of  tin- 
foil, and  containing  strong  sulphuric  acid  which  serves 
the  double  function  of  keeping  the  apparatus  dry  by 
absorbing  the  moisture  and  of  acting  as  an  internal 
coating  for  the  jar.  It  is  also  more  usual  to  throw  a 
spot  of  light  from  a  lamp  upon  a  scale  by  means  of  the 
little  mirror  (as  described  in  the  case  of  the  Mirror 
Galvanometer,  in  Art.  202),  than  to  adopt  the  subjective 
method  with  the  telescope,  which  only  one  person  at  a 
time  can  use.  When  the  instrument  is  provided  with 
replenishcr  and  gauge,  the  measurements  can  be  made  in 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM.  219 

terms  of  absolute  units,  provided  the  "  constant "  of  the 
particular  instrument  (depending  on  the  suspension  of 
the  needle,  si-e  and  position  of  needle  and  quadrants, 
potential  of  the  gauge,  etc.)  is  once  ascertained. 

263.  An  example  will  illustrate  the  mode  of  using  the  instru- 
ment. It  is  known  that  when  the  two  ends  of  a  thin  wire  are 
kept  at  two  different  potentials  a  current  flows  through  the  wire, 
and  that  if  the  potential  is  measured  at  different  points  along 
the  wire,  it  is  found  to  fall  off  in  a  perfectly  uniform  manner 
from  the  end  that  is  at  a  high  potential  down  to  that  at  the  low 
potential.  At  a  point  one  quarter  along  the  potential  will  have 
fallen  off  one  quarter  of  the  whole  difference.  This  could  be 
proved  by  joining  the  two  ends  of  the  wire  through  which  the 
current  was  flowing  to  the  terminals  of  the  Quadrant  Electro- 
meter, when  one  pair  of  quadrants  would  be  at  the  high 
potential  and  the  other  at  the  low  potential.  The  needle  would 
turn  and  indicate  a  certain  deflection.  Nov/,  disconnect  one  of 
the  pairs  of  quadrants  from  the  low  potential  end  of  the  wire, 
and  place  them  in  communication  with  a  point  one  quartet 
along  the  wire  from  the  high  potential  end.  The  needle  will 
at  once  indicate  that  the  difference  of  potential  is  but  one  quarter 
of  what  it  was  before. 

Often  the  Quadrant  Electrometer  is  employed  simply  as  a 
very  delicate  electrojw/^  in  systems  of  measurement  in  which  a 
difference  of  electric  potential  is  measured  by  being  balanced 
against  an  equal  and  opposite  difference  of  potential,  exact 
balance  being  indicated  by  there  being  no  deflection  of  the 
Electrometer  needle.  Such  methods  of  experimenting  are  known 
as  "  Null  Methods,"  or  "£?*?  Methods." 

2C4.  Dry-Pile  Electrometer. — The  principle  of 
symmetry  observed  in  the  Quadrant  Electrometer  was 
previously  employed  in  the  Electroscope  of  Bohnenberger 
— a  much  less  accurate  instrument — in  which  the  charge 
to  be  examined  was  imparted  to  a  single  gold  leaf,  placed 
symmetrically  between  the  poles  of  a  dry-pile  (Art.  182), 
toward  one  or  other  pole  of  which  the  leaf  was  attracted. 
Fechner  modified  the  instrument  by  connecting  the  + 
pole  of  the  dry-pile  with  a  gold  leaf  hanging  between 
two  metal  discs,  from  the  more  +  of  which  it  was  re* 


220  ELEMENTARY  LESSONS  ON        CCHAP.  iv. 

pelled.  The  inconstancy  of  dry -piles  as  sources  of 
electrification  led  Hankel  to  substitute  a  battery  of  a 
very  large  number  of  small  Daniell's  cells. 

265.  Capillary  Electrometers.  —  The  Capillary 
Electrometer  of  Lippmann,  as  modified  by  Dev/ar,  was 
described  in  Art.  225. 


LESSON  XXII. — Specific  Inductive  Capacity,  etc. 

266.  In  Lesson  VI.  it  was  shown  that  the  capacity 
of  a  Leyden  jar  or  other  condenser  depended  upon  the 
sue  of  the  conducting  coatings  or  surfaces,  the  thinness 
of  the  glass  or  other  dielectric  between  them,  and  upon 
the    particular    "  inductive   capacity "   of   the    dielectric 
used.      We  will   now  examine   the   subject   in  a   more 
rigorous  way.      In  Art.   246  it  was  laid  down  that  the 
capacity  of  a  conductor  was  measured  by  the  quantity 
of  electricity  required  to  raise  its  potential  to  un,ity  ;  or 
if  a  quantity  of  electricity  Q  raise  the   potential  from 
V  to  V*  then  its  capacity  is 

r  -     Q 
u  -  v^r? 

Now,  a  Leyden  jar  or  other  condenser  maj  be 
regarded  as  a  conductor,  in  which  (owing  to  the  parti- 
cular device  of  bringing  near  together  the  two  oppositely- 
charged  surfaces)  the  conducting  surface  can  be  made 
to  hold  a  very  large  quantity  of  electricity  without  its 
potential  (whether  +  or  - )  rising  very  high.  ThG 
capacity  of  a  condenser,  like  that  of  a  simple  con- 
ductor, will  be  measured  by  the  quantity  of  electricity 
required  to  produce  unh  rise  of  potential. 

267.  Theory    of   Spherical    Air -Con  denser. — 
Suppose    a   Leyden  jar  made  of  two  concentric    mstal 
sphereo,  one  inside  the  other,  the  space  bctweei    them 
being  filled  by  air.      The  inner  one,  A,  will  represent  the 
interior  coating  of  tinfoil,  and  the  outer  sphere,  B  (Fig. 


CHAP.  iv.J   ELECTRICITY  AND  MAGNETISM. 


221 


IO2),  will  represent  the  exterior  coating.  Let  the  radii 
of  these  spheres  be  r  and  / 
respectively.  Suppose  a  charge 
of  Q  units  to  be  imparted 
to  A;  it  will  induce  on  the 
inner  side  of  B  an  equal 
negative  charge  —  Q,  and  to 
the  ojtcr  side  of  B  a  charge 
+  Q  will  be  repelled.  This 
latter  is  removed  by  contact 
with  "  earth,"  and  need  be 
no  further  considered.  The 
potential1  at  the  centre  M, 
calculated  by  the  rule  given 
in  Art.  238,  will  be  Fig.  102. 

\T  Q        Q 

At  a  point  N,  outside  the  outer  sphere  and  quite  near  to 
it,  the  potential  will  be  the  same  as  if  these  two  charges, 
+  Q  and  -  Q,  were  both  concentrated  at  M.  Hence 

V      -  tQ-5  -,  o 

»  N    —  ~i         =    °- 

So  then  tfee  difference  of  potentials  will  be 
V    -v     -  £  -  Q  —  o  f'-'V 

•    V  *    TC      ~"~    ^^  /     ™~       '^      I  j      I   J 

«u  ->  ^  Y  \   fr     / 

O  IT' 

\\hcnce  i?  •    ?r    =:  -^ — • 

VM  —  \a  r  -  r 

But,  by  the  preceding  Article,  the  capacity  C  =•  v~ry;» 
therefore  C  =  ^ — . 

r  —r 

\Ve  see  from  this  foi-mula  that  the  capacity  of  the 
condenser  is  proportional  to  the  size  of  the  metal  globes, 
and  that  if  the  insulating  layer  is  very  thin, — that  is,  if 
r  be  very  nearly  as  great  as  r't  r'  —r  will  become  very 

1  The  student  must  remember  that  as  there  is  no  electric  force  within  a 
closed  conductor  the  potential  at  the  middle  is  just  the  same  as  at  any  other 
point  inside  ;  so  that  it  is  somewhat  a  stretch  of  language  to  talk  of  the 
middle  point  M  as  having  a  potential. 


222  ELEMENTARY  LESSONS  ON       [CHAP,  iv 

small,  and  the  value  of  the  expression  ~~  will  become 

very  great ;  which  proves  the  statement  that  the  capacity 
of  a  condenser  depends  upon  the  thinness  of  the  layer 
of  dielectric 

268.  Specific  Inductive  Capacity.  —  Cavendish 
was  the  first  to  discover  that  the  capacity  of  a  condenser 
depended  not  on  its  actual  dimensions  only,  but  upon 
the  inductive  flower  of  the  material  used  as  the  dielectric 
between  the  two  surfaces.  If  two  condensers  (of  any  of 
the  forms  to  be  described)  are  made  of  exactly  the  same 
size,  and  in  one  of  them  the  dielectric  be  a  layer  of  air, 
and  in  the  other  a  layer  of  some  other  insulating  sub- 
stance, it  is  found  that  equal  quantities  of  electricity 
imparted  to  them  do  not  produce  equal  differences -of- 
potentials ;  or,  in  other  words,  it  is  found  that  they  have 
not  the  same  capacity.  If  the  dielectric  be  sulphur, 
for  example,  it  is  found  that  the  capacity  is  about  three 
times  as  great ;  for  sulphur  possesses  a  high  inductive 
power  and  allows  the  transmission  -across  it  of  electro- 
static influence  three  times  as  well  as  air  does.  The 
name  specific  inductive  capacity1  was  assigned  by 
Faraday  to  the  ratio  between  the  capacities  of  two  con- 
densers equal  in  size,  one  of  them  being  an  air-condenser, 
the  other  filled  with  the  specified  dielectric.  The 
specific  inductive  capacity  of  dry  air  at  the  temperature 
o°  C,  and  pressure  76  centims.,  is  taken  as  the  standard 
and  reckoned  as  unity. 

Cavendish,  about  the  year  1775,  measured  the  specific 
inductive  capacity  of  glass,  bees -wax,  and  other  sub- 
stances, by  forming  them  into  condensers  between  two 
circular  metal  plates,  the  capacity  of  these  condensers 
being  compared  with  that  of  an  air  condenser  (resem- 
bling Fig.  30)  and  with  other  condensers  which  he 

1  The  name  is  not  a  very  happy  one, — specific  inductivity  would  have  been 
better,  and  is  the  analogous  term,  for  dielectrics,  to  the  term  "specific  con- 
ductivity "  used  for  conductors.  The  'term  dielectric  capacity  is  also  used  by 
some  modern  writers. 


CHAP,  iv.]  ELECTRICITY  AND  MAGNETISM. 


223 


a 


ailed  "  trial-plates."  He  even  went  so  far  as  to  com- 
pa-e  the  capacities  of  these  "  trial-plates  "  with  that  of  a 
sp'iere  of  12^  inches  diameter  hung  up  in  the  middle  of 
a  room. 

269.  Faraday's  Experiments. — In  1837  Faraday, 
who  did  not  know  of  the  then  un- 
published researches  of  Caven- 
dish, independently  discovered 
specific  inductive  capacity,  and 
measured  its  value  for  several 
substances,  using  for  this  pur- 
pose two  condensers  of  the  form 
shown  in  Fig.  103.  Each 
consiste'd  of  a  brass  ball  A; 
enclosed  inside  a  hollow  sphere 
of  brass  B,  and  insulated 
by  a  long  plug  of  shellac,  up 
which  passed  a  wire  terminating 
in  a  ball  a.  The  outer  sphere 
consisted  of  two  parts  which 
could  be  separated  from  each 
other  in  order  to  fill  the  hollow 
space  with  any  desired  material : 
the  experimental  process  then 
was  to  compare  their  capacities 
when  one  was  filled  with  the 
substance  to  be  examined,  the 
other  containing  only  dry  air. 
The  method  of  experimenting 

was  simple.  One  of  the  condensers  was  charged  with 
electricity.  It  was  then  made  to  share  its  charge  with  the 
other  condenser,  by  putting  the  two  inner  coatings  into 
metallic  communication  with  one  another,  the  outer 
coatings  also  being  in  communication  with  one  another. 
If  their  capacities  were  equal  they  would  share  the  charge 
equally,  and  the  potential  after  contact  would  be  just 
half  what  it  was  in  the  charged  condenser  before  con- 


Fig.  103. 


i24  ELEMENTARY  LESSONS  ON       (CHAP.  iv. 

tact.  If  the  capacity  of  one  was  greater  than  the  othe» 
the  final  potential  would  not  be  exactly  half  the  origins! 
potential,  because  they  would  not  share  the  charge 
equally,  but  in  proportion  to  their  capacities.  Tie 
potentials  of  the  charges  were  measured  before  aid 
after  contact  by  means  of  a  torsion  balance. 1  Faraday's 
results  showed  the  following  values: — Sulphur,  2-26: 
shellac,  2-0;  glass,  176  or  more. 

27O.  Recent  Researches. — Since  1870  large  addi- 
tions to  our  knowledge  of  this  subject  have  been  made. 
Gibson  and  Barclay  measured  the  inductive  capacity  of 
paraffin  by  comparing  the  capacity  of  an  air  condenser 
with  one  of  paraffin  by  means  of  a  sliding  condenser,  and 
a  divided  condenser  called  a  "  platymeter,"  using  a 
quadrant  electrometer  as  a  sensitive  electroscope  to 
adjust  the  capacity  of  the  condensers  exactly  to  equality. 
Wiillner,  Boltzmann,  and  others,  have  also  examined 
the  inductive  capacity  of  solid  bodies  by  several  methods. 
Hopkinson  has  examined  that  of  glass  of  various  kinds, 
using  a  constant  battery  to  produce  the  required  differ- 
ence of  potentials,  and  a  condenser  provided  with  a 
guard -ring  for  a  purpose  similar  to  that  of  the  guard- 
ring  in  absolute  electrometers.  Gordon  has  still  more 
recently  made  a  large  number  of  observations,  using  a 
delicate  apparatus  known  as  a  statical  "  induction 
balance,"  which  is  a  complicated  condenser,  so  arranged 
in  connection  with  a, quadrant  electrometer  that  when 
the  capacities  of  the  separate  parts  are  adjusted  to 
equality  there  shall  be  no  deflection  in  the  electrometer, 
whatever  be  the  amount  or  sign  of  the  actual  electrifi- 

1  The  value  of  the  specific  inductive  capacity  k  could  then  be  calculated 
as  follows : — 

Q  =  VC  =  V'C  +  V'Gt 

(where  C  is  the  capacity  of  the  first  apparatus  and  V  its  potential,  and  V' 
the  potential  after  communication  with  the  second  apparatus,  whose 
capacity  is  C*): 

hence  V  =  V  (i  -f  *) 

and  4-lr.V: 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  225" 

cation  employed,  for  the  moment.  This  arrangement, 
when  employed  in  conjunction  with  an  induction  coil 
(Fig.  148)  and  a  rapid  commutator,  admits  of  the  in- 
ductive capacity  being  measured  when  the  duration  of 
the  actual  charge  is  only  very  small,  the  electrification 
being  reversed  12,000  times  per  second.  Such  an  instru- 
ment, therefore,  overcomes  one  great  difficulty  besetting 
these  measurements,  namely,  that  owing  to  the  apparent 
absorption  of  part  of  the  charge  by  the  dielectric  (as 
mentioned  in  Art1.  53),  the  capacity  of  the  substance, 
when  measured  slowly,  is  different  from  its  "  instantane- 
ous capacity."  This  electric  absorption  is  discussed 
further  in  Art.  272.  The  amount  of  the  absorbed  charge 
is  found  to  depend  upon  the  time  that  the  charge  has 
been  accumulated.  For  this  reason  the  values  assigned 
by  different  observers  for  the  inductive  capacity  of  various 
substances  differ  to  a  most  perplexing  degree,  especially 
in  the  case  of  the  less  perfect  insulators.  The  following 
Table  summarises  Gordon's  observations  : 


Air    . 

Glass 

Ebonite 

Guttapercha 

Indiarubber 

Paraffin  (solid) 

Shellac 

Sulphur 


I'OO 

3-013     103-258 

2-284 

2-462 

2-220      to  2*497 
I  -9936 

274 
2-58 


Gordon's  values  would  probably  have  been  more 
reliable  had  the  plates  of  the  induction  balance  been 
provided  with  guard-rings  (Art.  248).  Hopkinson, 
whose  method  was  a  <l  slow  "  one,  found  for  glass 
much  higher  inductive  capacities,  ranging  from  6-5  to 
10-1,  the  denser  kinds  having  higher  capacities.  Row- 
land has  lately  examined  the  inductive  capacity  of 
plates  of  quartz  cut  from  a  homogeneous  crystal,  and 
finds  it  perfectly  devoid  of  electric  absorption.  Caven- 
dish observed  that  the  apparent  capacity  of  glass 


226 


ELEMENTARY  WESSONS  ON       [CHAP,  iv 


became  much  greater  at  those  temperatures  at  which  it 
begins  to  conduct  electricity.  Boltzmann  has  announced 
that  in  the  case  of  two  crystalline  substances,  Iceland 
spar  an3  sulphur,  the  inductive  capacity  is  different  in 
different  directions,  according  to  their  position"  with 
respect  to  the  axes  of  crystallisation. 

271.  Specific  Inductive  Capacity  of  Liquids 
and  Gases. — The  inductive  capacity  of  liquids  also 
has  specific  values.  The  following  table  is  taken  from 
the  data  of  Silow  and  of  Gordon  : — 


Turpentine  .       _^. 
Petroleum    . 
Bisulphide  of  Carbon 


2-16 

2-03  to  2-07 

1-81 


Faraday  examined  the  inductive  capacity  of  several 
gases  by  means  of  his  apparatus  (Fig.  103),  one  of  the 
condensers  being  filled  with  air,  the  other  with  the  gas 
which  was  let  in  through  the  tap  below  the  sphere  after 
exhaustion  by  an  air  pump.  The  method  was  too  rough, 
however,  to  enable  him  to  detect  any  difference  between 
them,  although  many  experiments,  were  made  with  dif- 
ferent pairs  of  gases  at  different  temperatures  and  under 
varying  pressures.  More  recently  Boltzmann,  and  inde- 
pendently Ayrton  and  Perry,  have  measured  the  specific 
inductive  capacities  of  different  gases  by  very  exact 
methods  ;  and  their  results  agree  very  fairly. 


Boltzmann. 

Ayrton  and  Perry. 

Air.                            . 
Vacuum   . 
Hydrogen 
Carbonic  Acid 
Olefiant  Gas 
Sulphur  Dioxide 

(1) 
(0-999410) 
0-999674 
1  -000356, 
I  -000722 

(I) 

(0-9985) 
0-9998 
1  -O008 

1  -0037 

272.  Mechanical  Effects  of  Dielectric  Stresa 
-That   different    insulating    substances   have    specific 


CHAP.  iv.J    ELECTRICITY  AND  MAGNETISM.  227 

inductive  power  sufficiently  disproves  the  idea  that 
induction  is  merely  an  "  action  at  a  distance,"  for  it  is 
evident  that  the  dielectric  medium  is  itself  concerned  in 
the  propagation  of  induction,  and  that  some  media  allow 
induction  to  take  place  across  them  better  than  others. 
The  existence  of  a  residual  charge  (Art.  53)  can  be 
explained  either  on  the  supposition  that  the  dielectric  is 
composed  of  heterogenous  particles  which  have  unequal 
conducting  powers,  as  Maxwell  has  suggested,  or  on  the 
hypothesis  that  the  molecules  are  actually  subjected  to 
a  strain  from  which,  especially  if  the  stress  be  long-con- 
tinued, they  do  not  recover  all  at  once.  Kohlrausch  and 
others  have  pointed  out  the  analogy  between  this  pheno- 
menon and  that  of  the  "elastic  recovery"  of  solid  bodies 
after  being  subjected  to  a  bending  or  a  twisting  strain. 
A  fibre  of  glass,  for  example,  twisted  by  a  certain  force, 
flies  back  when  released  to  almost  its  original  position, 
a  slight  sub -permanent  set  remains,  from  which,  how- 
ever, it  slowly  recovers  itself,  the  rate  of  its  recovery 
depending  upon  the  amount  'and  duration  of  the  original 
twisting  strain.  Hopkinson  has  shown  that  it  is  possible 
to  superpose  several  residual  charges,  even  charges  of 
opposite  signs,  which  apparently  "  soak  out  "  as  the 
strained  material  gradually  recovers  itself.  Perry  and 
Ayrton  have  also  investigated  the  question,  and  have 
shown  that  the  polarisation  charges  iri  voltameters  exhibit 
a  similar  recovery.1  Air  condensers  exhibit  no  residual 
charges. 

When  a  condenser  is  discharged  a  sound  is  often  heard. 
This  was  noticed  by  Sir  W.  Thomson  in  the  case  of  air 
condensers  ;  and  Varley  even  constructed  a  telephone  in 
which  the  rapid  charge  and  discharge  of  a  condenser 
gave  rise  to  distinct  tones. 

1  It  would  appear,  therefore,  probable  that  Maxwell's  suggestion  of  hetero- 
geneity of  structure,  as  leading  to  residual  electrification  at  the  bounding 
surface  of  the  particles  whose  electric  conductivities  differ,  is  the  true 
explanation  of  the  "  residual"  charge.  The  phenomenon  of  elastic  recovery 
may  itself  be  du*  to  heterogeneity  of  structure. 


428  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

As  to  the  precise  nature  of  the  molecular  or  mechanical 
operations  in  the  dielectric  when  thus  subjected  to  the 
stress  of  electrostatic  induction,  nothing  is  known.  One 
pregnant  experiment  of  Faraday  is  of  great  importance, 
by  showing  that  induction  is,  as  he  expressed  it,  "  an 
action  of  contiguous  particles."  In  a  glass  trough  (Fig. 

104),  is  placed 
some  oil  of  tur- 
pentine, in  which 
are  put  some  fibres 
of  dry  silk  cut  into 

„  small  bits.     Two 

Fig.  104. 

wires     pass     into 

the !  Liquid,  one  of  which  is  joined  to  earth,  the  other 
being-  put  into  connection  with  the  collector  of  an 
electrical  -  machine.  The  bits  of  silk  come  from  all 
parts  of'  the  liquid  and  form  a  chain  of  particles  from 
wire  to  wire.  On  touching  them  with  a  glass  rod  they 
resist  being  pushed  aside,  though  they  at  once  disperse 
if  the  supply  of  electricity  is  stopped.  Faraday  regarded 
this  as  typical  of  the  internal  actions  in  every  case  of 
induction  across  a1  dielectric,  the  particles  of  \\hich  he 
supposed  to  be  "polarised,"  that  is,  to  be  turned  into 
definite  positions,  each  particle  having  a  positive  and  a 
negative  end.  The  student  will  perceive  an  obvious 
analogy,  therefore,  between  the  condition  of  the  particles 
of  a  dielectric  across  which  electrostatic  induction  is 
taking  place,  and  the  molecules  of  a  piece  of  iron  or 
steel  when  subjected  to  magnetic  induction. 

Siemens  has  shown  that  the  glass  of  a  Leyden  jar  is 
sensibly  warmed  after  being  several  times  rapidly  charged 
and  discharged.  This  obviously  implies  that  molecular 
movement  accompanies  the  changes  of  dielectric  stress. 

273.  Electric  Expansion. — Fontana  noticed  that 
the  internal  volume  of  a  Leyden  jar  increased  when  it 
was  charged.  Volta  sought  to  explain  this  by  suggesting 
that  the  attraction  between  the  two  charged  surfaces 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM.  229 

compressed  the  glass  and  caused  it  to  expand  laterally. 
This  idea  had  previously  occurred  to  Priestley.  Dutei 
showed  that  the  amount  of  apparent  expansion  was 
inversely  proportional  to  the  thickness  of  the  glass,  and 
varied  as  the  square  of  the  potential  difference.  Quincke 
has  recently  shown  that  though  glass  and  some  other 
insulators  exhibit  electrical  expansion,  an  apparent  con- 
traction is  shown  by  resins  and  oily  bodies  under 
electrostatic  stress.  He  connects  with  these  properties 
the  production  of  optical  strain  and  of  double  refraction 
discovered  by  Kerr.  (See  Lesson  on  Electro-optics, 
ArtJ  386.) 

274.  Suomarine  Cables  as  Condensers.  —  A 
submarine  telegraph  cable  may  act  as  a  condenser,  the 
ocean  forming  the  outer  coating,  the  internal  wire  the 
inner  coating,  while  the  insulating  layers  of  guttapercha 
correspond  to  the  glass  of  the  Leyden  jar.  When  one 
end  of  a  submerged  cable  is  connected  to,  say,  the  +  pole 
of  a  powerful  battery,  +  electricity  flows  into  it.  Before 
any  signal  can  be  received  at  the  other  end,  enough 
electricity  must  flow  in  to  charge  the  cable  to  a  consider- 
able potential,  an  operation  which  may  in  the  case  of 
long  cables  require  some  seconds.  Faraday  predicted 
that  this  retardation  would  occur.  It  is,  in  actual  fact,  a 
serious  obstacle  to  signalling  with  speed  through  the 
Atlantic  cables  and  others.  Professor  Fleeming  Jenkin 
has  given  the  following  experimental  demonstration  of 
the  matter.  Let  a  mile  of  insulated  cable  wire  be  coiled 
up  in  a  tub  of  .water  (Fig.  105),  one  end,  N,  being 
insulated.  The  other  end  is  joined  up  through  a  long- 
coil  galvanometer,  G,  to  the  +  pole  of  a  large  battery, 
whose  —  pole  is  joined  by  a  wire  to  the  water  in  the  tub. 
Directly  this  is  done,  the  needle  of  the  galvanometer  will 
show  a  violent  deflection,  +  electricity  rushing  through  it 
into  the  interior  of  the  cable;  and  a  -  charge  being 
accumulated  on  the  outside  of  it  where  the  water  touches 
the  guttapercha.  For  perhaps  an  hour  the  flow  will  go 


230 


ELEMENTARY  LESSONS  ON       [CHAP.  tv. 


on,  though  diminishing,  until  the  cable  is  fully  charged. 
Now  remove  the  battery,  and  instead  join  up  a  and  b  by 
a  wire  ;  the  charge  in  the  cable  will  rush  out  through  the 


galvanometer,  which  will  show  an  opposite  deflection,  and 
the  residual  charge  will  continue  "  soaking  out "  for  a 
long  time. 

Since  the  speed  of  signalling,  and  therefore  the 
economical  working  through  a  cable,  depends  upon  its 
" capacity"  as  a  condenser,1  and  since  its  capacity 
depends  upon  the  specific  inductive  power  of  the  in- 
sulating substance  used,  Hooper's  compound,  which  has 
an  inductive  capacity  of  only  17,  and  is  cheap,  is  pre- 
ferred to  gutta-percha,  which  is  expensive,  and  has  a 
specific  inductive  capacity  as  high  as  2-46. 

275.  Use  of  Condensers. — To  avoid  this  retarda- 
tion and  increase  the  speed  of  signalling  in  cables  several 
devices  are  adopted.  Very  delicate  receiving  instruments 
are  used,  requiring  only  a  feeble  current ;  for  with  the 
feebler  batteries  the  actual  charge  given  to  the  cable  is 
less.  In  some  cases  a  key  is-  employed  which,  after 
every  signal,  immediately  sends  into  the  cable  a  charge 
of  opposite  sign,  to  sweep  out,  as  it  were,  the  charge  left 
behind.  Jn  duplex  signalling  (Lesson  XXXIX.)  the 

1  The  capacity  of  the  "  Direct"  Atlantic  cable  from  Pallinskelligs  (Ireland) 
to  Nova  Scotia  is  992  microfarad^ 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM.  2y. 

resistance  and  electrostatic  capacity  of  the  cable  have  to 
be  met  by  balancing  against  them  an  "  artificial  cable  " 
consisting  of  a  wire  of  equal  resistance,  and  a  condenser 
of  equal  capacity.  Messrs.  Muirhead  constructed  for 
duplexing  the  Atlantic  Cable  a  condenser  containing 
100,000  square  feet  (over  two  acres  of  surface)  of  tinfoil. 
Such  condensers  are  also  occasionally  used  on  telegraph 
lines  in  single  working  to  avoid  earth  currents.  They 
are  constructed  by  placing  sheets  of  tinfoil  between 
sheets  of  mica  or  of  paraffined  paper,  alternate  sheets  of 
foil  being  connected  together.  Small  condensers  of 
similar  construction  are  used  in  connection  with  induc- 
tion coils  (Fig.  148). 

276.  Practical  Unit  of  Capacity. — Electricians  adopt  a  unit 
of  capacity,  termed  one  farad,  based  on  the  system  of  electro- 
magnetic units.  A  condenser  of  one  farad  capacity  would  be 
raised  to  a  potential  of  one  volt  by  a  charge  of  one  coulomb  of 
electricity.1  In  practice  such  a  con- 
denser would  be  too  enormous  to  be 
constructed.  As  a  practical  unit 
of  capacity  is  therefore  chosen  the 
microfarad,  or  one  millionth  of  a 
farad ;  a  capacity  about  equal  to 
that  of  three  miles  of  an  Atlantic 
cable.  Microfarad  condensers  are 
made  containing  about  3600  square 
inches  of  tinfoil.  :  Their  general  form' 
is  shown  in  Fig.  106,  which  re-  Figriofi; 

presents  a  i  microfarad   condenser. 

The  two  brass  pieces  upon  the  ebonite  top  are  connected  re^ 
spectively  with  the  two  series  of  alternate  sheets  of  tinfoil.  The 
plug  between  them  serves  to  keeo  the  condenser  discharged 
v;hen  not^in  use. 

Methods  of  measunng'the  capacity^  of  a  condenser 
are  given  in  Art.  362. 

277.  Formulae   for  Capacities  of  Conductors 
and   Condensers.— The  following  formulae  give  the 

l  See  Note  on  Electromagnetic  Units,  Art,  jai.  Z 


231  ELEMENTARY  LESSORS  ON       [CHAP.  IV, 


capacity  of  condensers  of  all  ordinary  forms,  in  electro 
static  units  : — 

Sphere:  (radius  =  r.     See  Art.  247). 

C  =  r. 

Two  Concentric  Spheres:  (radii   r  and  /,   specific 
inductive  capacity  of  the  dielectric  =  k}. 

C  =  k—j — 

r> -r 

Cylinder :  (length  =  /,  radius  =  r\ 


Two  Concentric  Cylinders  :  (length  =  /,  specific  in- 
ductive  capacity  of  dielectric  =  /£,  internal  radius 
=  rt  external  radius  =  /. 


c      , 

\~  —  K 


Circular  Disc:  (radius  =  r>  thickness  negligible). 


Two  Circular  Discs:  (like  air  condenser,  Art.  48, 
radii  =  r,  surface  =  S,  thickness  of  dielectric  =  £, 
its  specific  inductive  capacity  =  k). 


or         C  =  k—. 

47T^ 

(The  latter  formula  applies  to  any  two  parallel  discs 
of  surface  S,  whether  circular  or  otherwise,  provided  they 
are  large  as  compared  with  the  distance  b  between 
them.) 

278.  Energy  of  Discharge  of  Ley-den  Jar  or 
Condenser.  —  It  follows  from  the  definition  of  potential, 
given  in  Art.  237,  that  in  bringing  up  one  +  unit  ol 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETIS>f.  233 

electricity  to  the  potential  V,  the  work  done  is  V  ergs. 
This  assumes,  however,  that  the  total  potential  V  is  not 
thereby  raised,  and  on  this  assumption  the  work  done 
in  bringing  up  Q  units  would  be  QV.  If,  however,  the 
potential  is  nothing  to  begin  with  and  is  raised  to  V  by 
tne  charge  Q,  the  average  potential  during  the  operation 
is  only  £V ;  hence  the  total  work  done  in  bringing  up 
the  charge  Q  from  zero  potential  to  potential  V  is  £QV 
ergs.  Now,  according  to  the  principle  of  the  con- 
servation of  energy,  the  work  done  in  charging  a  jar 
or  condenser  with  electricity  is  equal  to  the  work  which 
could  be  done  by  that  quantity  of  electricity  when  the 
jar  is  discharged.  Hence  a  |QV  represents  also  the 
energy  "of  the  discharge,  where  V  stands  for  the  dif- 
ference of  potential  between  the  two  coatings. 

Since  Q  =  VC,  it  follows  that  we  may  write  £QV  in 
the  form  ^.  That  is  to  say,  if  a  condenser  of  capacity 

C  is  charged  by  having  a  quantity  Q  of  electricity 
imparted  to  it,  the  energy  of  the  charge  is  proportional 
directly  to  the  square  of  the  quantity,  and  inversely  to 
the  capacity  of  the  condenser. 

If  two  equal  Leydea  jars  are  charged  to  the  same 
potential,  and  then  their  inside  and  outside  coatings  are 
respectively  joined,  their  united  charge  will  be  the  same 
as  that  of  a  jar  of  equal  thickness,  but  having  twice  the 
amount  of  surface. 

If  a  charged  Leyden  jar  is  placed— similarly  in  com- 
munication with  an  uncharged  jar  of  equal  capacity,  the 
charge  will  be  shared  equally  between  the  two  jars,  and 
the  passage  of  electricity  from  one  to  the  other  will  be 
evidenced  by  the  production  of  "a  spark  when  the 
respective  coatings  are  put  into  communication.  Here, 
however,  half  the  energy  of  the  charge  is  lost  in  the 
operation  of  sharing  the  charge,  for  each  jar  will  have 
only  £Q  for  its  charge  and  £V  for  its  potential ;  hence 
the  energy  of  the  charge  of  each  being  half  the  product 
of  charge  and  potential  will  only  be  one  quarter  of  the 


234  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

original  energy.  The  spark  which  passes  in  the 
operation  of  dividing  the  charge  is,  indeed,  evidence  of 
the  loss  of  energy ;  it  is  about  half  as  powerful  as  the 
spark  would  have  been  if  the  first  jar  had  been  simply 
discharged,  and  it  is  just  twice  as  powerful  as  the  small 
sparks  yielded  finally  by  the  discharge  of  each  jar  after 
the  charge  has  been  shared  between  them. 

The  energy  of  a  charge  of  the  jar  manifests  itself, 
as  stated  above,  by  the  production  of  a  spark  at  dis- 
charge ;  the  sound,  light,  and  heat  produced  being  the 
equivalent  of  the  energy  stored  up.  If  discharge  is 
effected  slowly  through  a  long  thin  wire  of  high  resistance 
the  air  spark  may  be  feeble,  but  the  wire  may  be 
perceptibly  heated.  A  wet  string  being  a  feeble  con- 
ductor affords  a  slow  and  almost  silent  discharge ;  here 
probably  the  electrolytic  conduction  of  the  moisture  is 
accompanied  by  an  action  resembling  that  of  secondary 
batteries  (Lesson  XXXVIII.)  tending  to  prolong  the 
duration  of  the  discharge. 

279.  Charge  of  Jars  arranged  in  Cascade. — 
Franklin  suggested  that  a  series  of  jars  might  be 
arranged,  the  outer  coating  of  one  being  connected  with 
the  inner  one  of  the  next,  the  outer  coating  of  the  last 
being  connected  to  earth.  The  object  of  this  arrange- 
ment was  that  the  second  jar  might  be  charged  with  the 
electricity  repelled  from  the  outer  coating  of  the  first, 
the  third  from  that  of  the  second,  and  so  on.  This 
"cascade"  arrangement,  however,  is  of  no  advantage, 
the  whole  charge  accumulated  in  the  series  being  only 
equal  to  that  of  one  single  jar.  For  if  the  inner  coating 
of  the  first  jar  be  raised  to  .V,  that  of  the  outer  coating 
of  the  last  jar  remaining  at  zero  in  contact  with  earth, 
the  difference  of  potential  between  the  outer  and  inner 
coating  of  any  one  jar  will  be  only  £  V,  where  n  is 
number  of  jars.  And  as  the  charge  in  each  jar  is  equal 
to  its  capacity  C,  multiplied  by  its  potential,  the  charge 
in  each  will  only  be  l-  CV^  and  in  the  whole  n  jars  the 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM,  235 

total  charge  will  be  n  -  CV,  or  CV,  or  equals  the  charge 
of  one  jar  of  capacity  C  raised  to  the  same  potential  V. 

LESSON  XXIII. — Phenomena  of  Discharge. 

280.  An  electrified  conductor  may  be  discharged  in 
at  least  three  different  ways,  depending  on  the  medium 
through  which  the  discharge  .is  effected,  and  varying 
with  the  circumstances  of  the  discharge. 

281.  Disruptive    Discharge.  —  In   the   preceding 
Lesson  it  has  been  shown  that  induction  across  a  non- 
conducting medium  is  always  accompanied  by  a  mechani- 
cal stress  upon  the  medium.      If  this  stress  is  very  great 
the  non-conducting  medium  will  suddenly  give  way  and 
a  spark  will  burst  across  it.     Such  a  discharge  is  called 
a  "  disruptive  "  discharge. 

A  very  simple  experiment,  carefully  considered,  will 
set  the  matter  in  a  clear  light.  Suppose  a  brass  ball 
charged  with  +  electricity  to  be  hung  by  a  silk  siring 
above  a  metal  plate  lying  on  the  ground.  If  we  lower 
down  the  suspended  ball  a  spark  will  pass  between  it 
and  the  plate  when  they  come  very  near  together,  and 
the  ball  will  then  be  found  to  have  lost  all  its  previous 
charge.  It  was  charged  with  a  certain  quantity  of 
electricity,  and  as  it  had,  when  suspended  out  of  the 
range  of  other  conductors,  a  certain  capacity  (numeri- 
cally equal  to  its  radius  in  centimetres),  the  electricity 
on  it  would  be  at  a  certain  potential  (namely  =  ^),  and 
the  charge  would  be  distributed  with  a  certain  surface 
density  all  over  it.  The  plate  lying  on  the  earth  would 
be  all  the  while  at  zero  potential.  But  when  the  sus- 
pended ball  was  lowered  down  towards  the  plate  the 
previous  state  of  things  was  altered.  In  the  presence 
of  the  +  charge  of  the  ball  the  potential1  of  the  plate 

1  The  student  must  remember  that,  by  the  definition  of  potential  in 
Art.  237,  the  potential  at  a  point  is  the  sitm  of  all  the  separate  quantities  of 
electricity  near  it,  divided  each  by  its  distance  from  the  point. 


236  ELEMENTARY  LESSONS  ON       [CHAP.  iyf 

would  rise,  were  it  not  that,  by  the  action  termed 
induction,  just  enough  negative  electrification  appears  on 
it  to  keep  its  potential  still  the  same  as  that  of  the  earth. 
The  presence  of  the  induced  negative  electricity  on  the 
plate  will  attract  the  +  electricity  of  the  ball  downwards, 
and  alter  the  distribution  of  the  electricity  on  the  ball, 
the  surface  -  density  becoming  greater  at  the  under 
surface,  and  less  on  the  upper.  The  capacity  of  the 
ball  will  be  increased,  and  therefore  its  potential  will 
fall  correspondingly.  The  layer  of  air  between  the  ball 
and  the  plate  is  acting  like  the  glass  of  a  Leyden  jar. 
The  more  the  ball  is  lowered  down  the  greater  is  the 
accumulation  of  the  opposite  kinds  of  electricity  on  each 
side  of  the  layer  of  air,  and  the  stress  across  the  layer 
becomes  greater  and  greater,  until  the  limit  of  the 
dielectric  strength  is  reached ;  the  air  suddenly  gives 
way  and  the  spark  tears  a  path  across.  The  greater 
the  difference  of  potential  between  the  two  bodies,  the 
thicker  will  be  the  layer  which  can  thus  be  pierced,  and 
the  longer  will  be  the  spark. 

282.  Conductive   Discharge.  —  If  the  discharge 
takes  place  by  the   passage  of  a   continuous   current, 
as  when  electricity  flows  through  a  thin  wire  from  the 
collector  of  a  machine  back  to  the  rubbers,  or  from  the 
positive  pole  of  a  battery  to  the  negative  pole,  the  opera- 
tion is  termed  a  "  conductive  "  discharge.     The  laws 
of  the  conductive  discharge  are  explained  in   Lessons 
XXIX.  and  XXX. 

283.  Oonvective   Discharge. — A  third  kind   of 
discharge,  differing  from  either  of  those  above  mentioned, 
may  take  place,  and  occurs  chiefly  when  electricity  of  a 
high  potential  discharges  itself  at  a  pointed  conductor 
by  accumulating  there  with  so  great  a  density  as  to 
electrify  the  neighbouring  panicles  of  air  ;  these  particles 
then  flying  off  by  repulsion,  conveying  away  part  of  the 
charge   with   them.      Such    connective   discharges-  may 
occur  either  in  gases  or  in  liquids,  but  are  best  mani- 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  23* 

Tested  in  air  and  other  gases  at  a  low  pressure,'' in  tubes 
exhausted  by  an  air  pump. 

The  discharge  of  a  quantity  of  electricity  in  any  of 
the  above  ways  is  always  accompanied  by  a  transform- 
ation of  its  energy  into  energy  of  some  other  kind, — 
sound,  light,  heat,  chemical  actions,  and  other  pheno- 
mena being  produced.  These  effects  must  be  treated  in 
detail. 

284.  Mechanical  Effects.  —  Chief  amongst  the 
mechanical  effects  of  the  .disruptive  spark  discharge  is 
the  shattering  and  piercing  of  glass  and  other  insulators. 
The  dielectric  strength  of  glass,  though  much  greater 
than  that  of  air,  is  not  infinitely  great.  A  slab  of  glass 
3  inches  thick  has  been  pierced  by  the  discharge  of  a 
powerful  induction-coil.  The  so-called  "toughened" 
glass  has  a  greater  dielectric  strength  than  ordinary 
glass,  and  is  more  difficult  to  pierce.  A  sheet  of  glass 
may  be  readily  pierced  by  a  spark  from  a  large  Leyden 
jar  or  battery  of  jars,  by  taking  the  following  precau- 
tions : — The  glass  to  be  pierced  is  laid  upon  a  block  of 
glass  or  resin,  through  which  a  wire  is  led  by  a  suitable 
hole,  one  end  of  the  wire  being  connected  with  the  outer 
coating  of  the  jar,  the  other  being  cut  off  flush  with  the 
surface.  Upon  the  upper  surface  of  the  sheet  of  glass 
that  is  to  be  pierced  another  wire  is  fixed  upright,  its 
end  being  exactly  opposite  the  lower  wire,  the  other 
extremity  of  this  wire  being  armed  with  a  metal  knob  to 
receive  the  spark  from  the  knob  of  the  jar  or  discharger. 
To  ensure  good  insulation  a  few  drops  of  paraffin  oil,  or 
of  olive  oil,  are  placed  upon  the  glass  round  the  points 
where  the  wires  touch  it.  A  piece  of  dry  wood  similarly 
treated  is  split  by  a  powerful  spark. 

If  a  spark  is  led  through  a  tightly  corked  glass  tube 
containing  water,  the  tube  will  be  shattered  into  small 
pointed  fragments  by  the  sudden  expansion  of  the 
liquid. 

The    mechanical    action   of  the   brush   discharge  at 


238  ELEMENTARY  LESSONS  ON       [CHAP,  iv- 

points  is  mentioned  in  Art.  43,  and  the  mechanical 
effects  of  a  current  of  electricity  were  described  in 
Lesson  XIX. 

285.  Lullin's   Experiment. — If  a  piece  of  card- 
board be  perforated  by  a  spark  between  two  metal  points, 
two  curious  facts  are  observed.    Firstly,  there  is  a  slight 
burr  raised  on  each  side,  as  if  the  hole  had  been  pierced 
from  the  middle  outwards.     Secondly r,  if  the  two  points 
are  not  exactly  opposite  one  another  the  hole  is  found 
to  be  nearer  the  negative  point.      But  if  the  experiment 
is  tried  under  the  air  pump  in  a  vacuum,  there  is  no 
such  displacement   of  the    hole ;    it   is   then   midway 
exactly. 

286.  Chemical    Effects. — The,  chemical   actions 
produced  by  currents  of  electricity  have  been  described 
in  Lessons  XIV.  and  XViII.     Similar  actions  can  be 
produced  by  the  electric  spark,  and  by  the  silent  glow 
discharge  (see  Art.  290).     Faraday  showed,  indeed,  that 
all  kinds  of  electricity  from,  different  sources  produced  the 
same  kinds  of  chemical  actions,  and  he  relied  upon  this 
as  one  proof  of  the  essential  identity  of  the  electricity 
produced  in  different  ways.      If  sparks  from  an  electric 
machine  are  received  upon  a  piece  of  white,  blotting- 
paper  moistened  with  a  solution  of  iodide  of  potassium, 
brown  patches  are  noticed  where  the  spark  has  effective 
a  chemical  decomposition  and  liberated  the  iodine. 

When  a  stream  of  sparks  is  passed  through  moist  air 
in  a  vessel,  the  air  is  found  to  have  acquired  the  property 
of  changing  to  a  red  colour  a  piece  of  paper  stained 
blue  with  litmus.  This,  Cavendish  showed,  was  due  to 
the  presence  of  nitric  a.cid,  produced  by  the  chemical 
union  of  the  nitrogen  and  oxygen  of  the  air.  The  effect 
is  best  shown  with  the  stream  of  sparks  yielded  by  a 
small  induction  coil  (Fig.  148),  in  a  vessel  in  which  the 
air  has  been  compressed  beyond  the  usual  atmospheric 
pressure. 

The  spark  will  decompose  ammonia  gas,  and  olefiant 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  239 

gas,  and  it  will  also  cause  chemical  combination  to  take 
place  with  explosion,  when  passed  through  detonating 
mixtures  of  gases.  Thus  equal  volumes  of  chlorine  and 
hydrogen  are  exploded  by  the  spark.  So  are  oxygen  and 
hydrogen  gases,  when  mixed  in  the  proportion  of  two 
volumes  of  the  latter  to  one  of  the  former.  Even  the 
explosive  mixture  of  common  coal  gas  mixed  with  from 
four  to  ten  times  its  own  volume  of  common  air,  can  be 
thus  detonated.  A  common  experiment  with  the  so- 
called  electric  pistol  consists  in  filling  a  small  brass  vessel 
with  detonating  gases  and  then  exploding  them  by  a 
spark.  The  spark  discharge  is  sometimes  applied  to 
the  firing  of  blasts  and  mines  in  military  operations,  a 
small  quantity  of  fulminating  powder  being  placed  in 
the  path  of  the  spark  to  kindle  the  larger  charge  of 
gunpowder  or  other  explosive.  (See  also  Art.  370.) 

287.  Physiological    Effects. — The    physiological 
effects  of  the  current  have  been  described  in   Lesson 
XIX.     Those  produced  by  the  spark  discharge  are  mor-3 
sudden  in  character,  but  of  the  same  general  nature. 
The  bodies  of  persons  killed  by  the  lightning  spark 
frequently  exhibit  markings  of  a  reddish  tint  where  the 
discharge  in  passing  through  the  tissues  has  lacerated  or 
destroyed  them.     Sometimes  these  markings  present  a 
singular  ramified  appearance,  as  though  the  discharge 
had  spread  in  streams  over  the  surface  at  its  entry. 

288.  Calorific    Effects.-- The    flow -of  electricity 
through  a  resisting  medium  is  in  every  case  accompanied 
by  an  evolution  of  heat.     The  laws  of  heating  due  to 
currents  are  given  in  Art.  367.     The  disruptive  discharge 
is  a  transfer  of  electricity  through  a  medium  of  great 
resistance  and  accompanied  by  an   evolution  of  heat. 
A  few  drops  of  ether  in  a  metallic   spoon  are  easily 
kindled  by  an  electric  spark.    The  spark  from  an  electric 
machine,  or  even  from  a  rubbed  glass  rod,  is  hot  enough 
to  kindle   an  ordinary  gas-jet.      In  certain  districts  of 
America,  during  the  driest  season  of  the  year,  the  mere 


240  ELEMENTARY  LESSONS  ON       [CHAP,  iv, 

rubbing  of  a  person's  shoes  against  the  carpet,  as  he 
shuffles  across'  the  floor,  generates  sufficient  electricity  to 
enable  sparks  to  be  drawn  from  his  body, -and  he  may 
light  the  gas  by  a  single  spark  from  his  outstretched 
finger.     Gunpowder  can  be  fired  by  the  discharge  of  a 
Leyden  jar,  but  the  spark  should  be  retarded  by  being 
passed  through  a  wet  thread,  otherwise  the  powder  will 
simply  be  scattered  by  the  spark. 
-The   Electric  Air-  Thermometer ^  invented   by;  Kin- 
nersley,1  serves  to  investigate  the  heating  powers  of  the 
discharge.     It  consists,  of  a  glass  vessel  enclosing  air, 
and  communicating  with  a  tube  partly  filled  with  water 
or  other  liquid,- in  order  to  observe  changes  of  volume  or 
of  pressure.     Into  this  vessel  are  led  two  metal  rods, 
between  which  is  suspended  a  thin  wire,  or  a  filament 
of  gilt  paper ;  or  a  spark  can  be  allowed  simply  to  cross 
between  them.    When  the  discharge  passes  the  enclosed 
air  is  heated,  expands,  and  causes  a  movement  of  the 
indicating  column  of  liquid.     Mascart  has  further  de- 
veloped .the  instrument  by  making  it    self- registering. 
The  results   of  observation  with  these  instruments  are 
as  follows  : — The  heating  effect  produced,  by  a  given 
charge  in  a  wire  of  given  length  is  inversely  proportional 
to  the  square  of  the  area  of  the  cross  section  of  the  wire. 
The  heating  effect  is  greater,  the  slower  the  discharge. 
The  total  heat   evolved  is  jointly  proportional   to  the 
charge,  and  to  the  potential  through  which  it  falls.     In 
fact,  if  the  entire  'energy  of  the  discharge  is  expended 
in  producing  heat,  and  in  doing  no  other  kind  of  work, 
then  the  heat  developed  will  be  the  thermal  equivalent 

of  \  QV,  or  will  be  -^    -  units  of  heat,  where  J  repre- 
sents the  mechanical  equivalent  of  heat,- (J  —  42  million; 

l  This  instrument  differs  in  no  essential  respect  from  that  deviccd  ninety 
years. later  by  Riess,  to  whom  the  instrument  is  often  accredhc_.  T^iess, 
however,  deduced  quantitative  laws,  while  Kinnersley  concerned  him 
self  with  qualitative  observations.  Caow  Harris  r'"o  anticipated  Riess  in 
s- veral  points  of  his.  researches. 


CKAP.  iv.]    ELECTRICITY  AND  MAGNETISM.  241 

since  42  x   io6  ergs  -=  i  gramme-water-degree  of  heat), 
and  Q  and  V  are  expressed  in  C.  G.  S.  units. 

When  a  powerful  discharge  takes  place  through  very 
thin  wires,  they  may  be  heated  to  redness,  and  even 
fused  by  the  heat  evolved.  Van  Marum  thus  once 
heated  70  feet  of  wire  by  a  powerful  discharge.  A 
narrow  strip  of  tinfoil  is  readily  fused  by  the  charge  of 
a  large  Leyden  jar,  or  battery  of  jars.  A  piece  of  gold 
leaf  is  in  like  manner  volatilised  under  the  sudden  heat- 
ing of  a  powerful  discharge ;  and  Franklin  utilised  this 
property  for  a  rude  process  of  multiplying  portraits  or 
other  patterns,  which,  being  first  cut  out  in  card,  were 
reproduced  in  a  silhouette  of  metallic  particles  on  a 
second  card,  by  the  device  of  laying  above  them  a  film 
of  gold  or  silver  leaf  covered  again  with  a.  piece  of  card 
or  paper,  and  then  transmitting  the  charge  of  a  Leyden 
battery  through  the  leaf  between  the  knobs  of  a  universal 
discharger. 

289.  Luminous  Effeota — The  luminous  effects 
of  the  discharge  exhibit  many  beautiful  and  interesting 
variations  under  different  conditions.  The  spark  of  the 
disruptive  discharge  is  usually  a  thin  brilliant  streak  of 
light.  When  it  takes  place  between  two  metallic  balls, 
separated  only  by  a  short  interval,  it  usually  appears 
as  a  single  thin  and  brilliant  line.  If,  however,  the 
distance  be  as  much  as  a  few  centimetres,  the  spark 
takes  an  irregular  zig-zag  form.  In  any  case  its  path  is 
along  the  line  of  least  resistance,  the  presence  of  minute 
motes  of  dust  floating  in  the  air  being  quite  sufficient  to 
determine  the  zig-zag  character.  In  many  cases  the 
spark  exhibits  curious  ramifications  and  forkings,  o' 
which  an  illustration  is  given  in  Fig.  107,  which  is  drawr 
of  one  eighth  of  the  actual  size  of  the  spark  obtained 
from  a  Cuthbertson's  electrical  machine.  The  discharge, 
from  a  Leyden  jar  affords  a  much  brighter,  shorter, 
noisier  spark  than  the  spark  drawn  direct  from  the 
rollector  of  a  machine.  The  length  (see  Art.  291) 


242  ELEMENTARY  LESSONS  ON      [CHAP.  iv. 

depends  upon  the  potential,  and  upon  the  pressure  and 
temperature  of  the  air  in  which  the  discharge  takes 
place.  The  brilliance  depends  .chiefly  upon  the  quantity 


Fig.  107. 

of  electricity  discharged.  The  colour  of  the  spark  varies 
with  the  nature  of  the  metal  surfaces  between  which 
the  discharge  takes  place.  Between,  copper  or  silver 
terminals  the  spark  takes  a  green  tint,  while  between 
iron  knobs,  it  is  of  a  reddish  hue.  Examination  with 
the  spectroscope  reveals  the  presence  in  the  spark  of  the 
rays  characteristic  of  the  incandescent  vapours  of  the 
several  metals  ;  for  the  spark  tears  away  in  its  passage 
small  portions  of  the  metal  surfaces,  and  volatilises 
them. 

29O.  Brush  Discharge:  Glow  Discharge.  —  If 
an  electric  machine  is  vigorously  worked,  but  no  sparks 
be  drawn  from  its  collector,  a  fine  diverging  brtish  of 
pale  blue, light  can  be  seen  (in  a  dark  room)  streaming 
from  the  brass  ball  at  the  end  of  it  farthest  from  the 
collecting  comb :  a  hissing  or  crackling  sound  always 
accompanies  this  kind  of  discharge.  The  brush  dis- 
charge consists  of  innumerable,  fine  twig-like  ramifications, 
presenting  a  form  of  which  Fig.  108  gives  a  fine  example. 
The  brightness  and  sl^e  of  the  brush  is  increased  by 
holding  a  flat  plate  of  metal  a  little  way  from  it.  With 
a  smaller  ball,  or  with  a  bluntly  pointed  wire,  the  brush 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  243 

appears,  smaller,  but  is  more  distinct  and  continuous. 
The  brush  discharge  is  larger  and  more  ramified  when  a 
positive  charge  is  escaping-,  than  when  the  electrification 


Fig.  108.  \ 

is  negative.  Wheatstone  found  by  using  his  rotating 
mirror  that  the  brush  discharge  is  really  a  series  of 
successive  partial  sparks  at  rapid  intervals. 

If  the  blunt  or  rounded  conductor  be  replaced  by  a 
pointed  one,  the  brush  disappears  and  gives  place  to  a 
quiet  and  continuous  glow  Where  the  electrified  particles 
of  air  are  streaming  away  at  the  point.  If  these  con- 
vection-streams are  impeded  the  glow  may  once  more 
give  place  to  the  brush.  Where  a  negative  charge  is 
being  discharged  at  a  point,  the  glow  often  appears  to 
be  separated  from  the  surface  of  the  conductor  by  a  dark 
space,  where  the  air,  without  becoming  luminous,  still 
conveys  the  electricity.  This  phenomenon,  to  which 
Faraday  gave  the  name  of  the  "  dark  "  discharge^  is  very 
well  seen  when  electricity  is  discharged  through  rarefied 
r.ir  and  other  gases  in  vacuum  tubes. 

291.  Length  of  Sparks. — Roughly  speaking,  the 


244  ELEMENTARY  LESSONS  ON       iCUAP.  IV. 

length  of  spark  between  two  conductors  increases  with 
the  difference  between  their  potentials.  It  is  also  found 
to  increase  when  the  pressure  of  the  air  is  diminished. 
Riess  found  the  distance  to  increase  in  a  proportion  a 
little  exceeding  that  of  the  difference  of  potentials,  Sir 
W.  Thomson  measured  by  means  of  an  "  absolute  elec- 
trometer" (Art.  261)  the  difference  of  potential  necessary 
to  produce  a  spark  discharge  between  two  parallel  plates 
at  different  distances.  His  precise  experiments  confirm 
Riess's  observation.  Thus,  to  produce  a  spark  at  -i  of 
a  millimetre  distance,  the  difference  of  potential  must  be 
27  (arbitrary)  units  ;  at  -5  millim.  7-3  units ;  at  I  millim. 
12-6  units;  and  at  1*5  millims.  17-3  units.  De  la  Rue 
and  Miiller  have  found  with  their  great  battery  (Art.  174) 
that  with  a  difference  of  potential  of  1000  volts  the  strik- 
ing distance  of  the  spark  was  only  -0127  centimetres  (or 
about  T&S  of  an  inch),  and  with  a  difference  of  10,000 
volts  only  1-369.  Their  1 1,000  silver  cells  gave  a  spark 
of  i '59  centim.  (about  §  of  an  inch)  long.  To  produce 
a  spark  one  mile  long,  through  air  at  the  ordinary 
pressure,  would  therefore  require  a  difference  of  potential 
exceeding  that  furnished  by  1,000,000,000  Daniell's  cells ! 
The  length  of  the  spark  differs  in  different  gases,  being 
nearly  twice  as  long  in  hydrogen  as  in  air  at  the  same 
density,  and  longer  in  air  than  in  carbonic  acid  gas. 

In  rarefied  air  the  spark  is  longer.      Snow   Harris 
stated  that  the  length  of  spark  was  inversely  proportional 
to  the  pressure,  but  this  law  is  not  quite  correct,  being 
approximately  true  only  for  pressures  between  that   of 
eleven   inches  of  mercury  and  that  of  30  inches  (one 
atmosphere).     At  lower  pressures,  as  Gordon  has  lately 
shown,  a  greater  difference  of  potential  must  be  used  to 
produce  a  spark  than  that  which   would  accord   with 
Harris's   law.      From  this  it  would  appear   that   th>'a 
layers  of  air  oppose  a  proportionally  greater  rtsistance 
to  the  piercing  power  of  the  spark  than  thick  layers  and 
possess  greater  dielectric  strength. 


CHAP,  iv.j    ELECTRICITY  AND  MAGNETISM.  245 


A  perfect  vacuum  is  a  perfect  insulator — no  spark 
cross  it.  it  is  possible  to  exhaust  a  tube  so  perfectly 
that  none  of  our  electric  machines  or  appliances  can 
send  a  spark  through  the  vacuous  space  even  over  so 
short  a  distance  as  one  centimetre. 

On  the  other  hand  a  great  increase  of  pressure  also 
increases  the  dielectric  strength  of  air,  and  causes  it  to 
resist  the  passage  of  a  spar-k.  .  Cailletet  compressed  dry 
air  at  40  10.50  atmospheres'  pressure,  and  found  that 
even  the  spark,  of  a  powerful  induction  con  failed  to  cross 
a  space  of  -05  centimetre  wide.  The  length  of  the  spark 
(in  air),  is  "also  affected  by  temperature,  sparks  being 
longer  and  straighter  through  hot  air  than  through  cold. 

Flames  and  currents  of  very  hot  air,  such  as  those 
rising  fiom  a  red-hot  piece  of  iron,  are  extremely  good 
conductors  of  electricity,  and  act  even  better  than 
metallic  points  in  discharging  a  charged  conductor. 
Gilbert  sbowe'd"  that  an  Electrified  body  placed  near  a 
flame  lost  its  charge ;  and  -the  very  readiest  way  to  rid 
the  surface  of  a  charged -body  of  low  conducting  power 
of  a  charge  imparted  to  it  by  friction  or  otherwise,  is  to 
pass  it  through  the  -flame  of  a  spirit-lamp.  Faraday 
found  negative  electrification  to  be  thus  more  easily  dis- 
charged than  positive.  Flames  powerfully  negatively 
electrified  are.'  repelled  from  "conductors,  though  not  so 
when  positively  electrified.  Sir  W.  Grove  has  shown 
that  a  current  is  set  up  in  a  •platinnm  wire,  one  end 
of  which  touches  the  tip,  and  the  other  the  base,  of  a 
(lame. 

292.  Discharges  in  Partial  Vacua — If  the  dis- 
charge take  place  in  glass  tubes  or  vessels  .from  which 
the  air  has  been  partially  exhausted,  many  remarkable 
and  beautiful  luminous  phenomena  are  produced.  A  com- 
mon form  of  vessel  is  the  "  electric  egg  "  (Fig.  1 50),  a 
sort  of  oval  bottle  that  can  be  screwed  to  an  air-pump,  and 
furnished  with  brass  knobs  to  lead  in  the- sparks.  More 
often  "  vacuum  tubes,"  such  as  those  manufactured  by 


246  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 

me  celebrated  Geissler,  are  employed.  These  are  merely 
tubes  of  thin  glass  blown  into  bulbous  or  spiral  forms, 
provided  with  two  electrodes  of  platinum  wire  fused  into 
the  glass,  and  sealed  'off  after  being  partially  exhausted 
of  air  by  a  mercurial  air-pump.  Of  these  Geissler  tubes 
the  most  useful  consist  of  two  bulbs  joined  by  a  very 
narrow  tube,  the  luminous  effects  being  usually  more 
intense  in  the  contracted  portion.  Such  tubes  are 
readily  illuminated  by  a  spark  from  an  electrophorus  or 
electric  machine  $  but  it  is  more -common  to  work  them 
with  the  spark  of  an  induction  coil  (Fig;  148). 

Through  such  tubes,  before  exhaustion,  the  spark  passes 
without  any  unusual  phenomena  being  produced.  As 
the  air  is  exhausted  the  sparks  become  less  sharply 
defined,  and  widen  out  to  occupy  the  whole  tube, 
becoming  pale  in  tint  and  nebulous  -in  form.  The 
negative  electrode  exhibits  a  beautiful  bluish  or  violet 
glow,  separated  from  the  conductor  by  a  narrow  dark 
interval,  while  at  the  positive  electrode  a  single  small 
bright  star  of  light  is  all  that  remains.  Frequently  the 
light  breaks  up  into  a  set  of  strife  t  or  patches  of  light  of 
a  cup-like  form,  which  vibrate  to  and  fro  between  darker 
spaces.  In  nitrogen  gas  the  violet  aureole  glowing 
around  the  negative  pole  is  very  bright,  the  rest  of  the 
light  being  rosy  in  tint.  In  oxygen  the  difference  is  not 
so  marked.  In  hydrogen  gas  the  tint  of  the  discharge 
is  bluish,  except  where  the  tube  is  narrow,  where  a 
beautiful  crimson  may  be  seen.  With  carbonic  acid  gas 
;he  light  is  remarkably  white.  Particles  of  metal  are 
orn  off  from  the  negative  electrode,  and  projected  from 
.is  surface.  The  negative  electrode  is  also  usually  the 
hotter  when  made  of  similar  dimensions  to  the  positive 
electrode.  It  is  also  observed  that  the  light  of  these 
discharges  in  vacuo  is  rich  in  tfeose  rays  which  produce 
phosphorescence  and  fluorescence.  Many  beautiful 
effects  are  therefore  produced  by  blowing  tubes  in 
uranium  glass,  which  fluoresces  with  a  fine  green  light, 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  247 

and  by  placing  solutions  of  quinine  or  other  fluorescent 
liquids  in  outer  tubes  of  glass. 

293.  Phenomena  in  High  Vacua. — Crookes  has 
found  that  when  exhaustion  is  carried  to  a  very  high 
degree,   the   dark   space   separating  the   negative  glow 
from   the  negative   pole   increases   in  width ;  and  that 
across  this  space  electrified  molecules  are  projected  in 
parallel  paths  normally  to  the  surface  of  the  electrode. 
The  chief  point  relied  upon  for  this   theory  is,  that  if 
exhaustion   be  carried  to  such  a  high  degree  that  the 
dark   space   fills  the   entire    tube   or  bulb,  and  bodies 
(whether  opaque  or  transparent)  be  then  interposed  in 
front  of  the  electrode,  sharply  defined  shadows  of  these 
bodies  are  projected  upon  the  opposite  wall  of  the  vessel, 
as  if  they  stopped  the  way  for  some  of  the  flying  mole- 
cules, and  prevented  them  from   striking  the  opposite 
walh      Lightly -poised  vanes  are   also   driven   round   if 
placed  in  the  path  of  the  discharge.     Holtz  has  more 
recently  produced  "  electric  shadows,"  by  means  of  dis- 
charges in  air  at  ordinary  pressure,  between  the  poles  of 
his  well-known  machine  (Fig.  29),  the  discharge  taking 
place  between  a  point  and  a  disc  covered  with  silk,  on 
which  the  shadows  are  thrown. 

294.  Striae. — The  siiice  or  stratifications  have  been  examined 
very  carefully  by  Gassiot.  by  Spottiswoode,  and  Ly  De  la  Rue. 
The  principal  facts  hitherto  gleaned  are  as  follow  : — The  striae 
originate  at  the   positive   electrode  at  a  certain  pressure,  and 
become  more  numerous,  as  the  exhaustion  proceeds,  up  to  a 
certain  point,  when  they  become  thicker  and  diminish  in  number, 
until  exhaustion  is  carried  to  such  a  point  that  no  discharge  will 
pass.     The  striae  are  hotter  than  the  spaces  between  them.     The 
number  and  position  of  the  striae  vary,  not  only  with  the  exhaus- 
tion but  with  the  difference  of  potentials  of  the  electrodes.    When 
striae  are  produced  by  the  intermittent  discharges  of  the  induction 
roil,  examination  of  them  in  a  rotating  mirror  reveals  that  they 
move  forward  from  the  positive  electrode  towards  the  negative. 

Schuster  has  recently  shown  that  the  discharge  of  electricity 
through  gases  is  a  process  resembling  that  of  electrolysis  (Art. 
418),  being  accompanied  by  breaking  up  of  the  gaseous  mole- 


248  ELEMENTARY  LESSONS  ON      [CHAP.  iv. 

cules  and  incessant  interchanges  of  atoms  bctv/een  them.  The 
production  of  ozone  (Art.  208)  and  the  phenomena  noticed  at  the 
negative  electrode  (Art.  292)  certainly  give  support  to  this  view. 
The  discharges  in  vacuum  tubes  are  affected  by  the  magnet 
at  all  degrees  of  exhaustion,  behaving  like  flexible  conductors. 
Under  certain  conditions  also,  the  discharge  is  sensitive  to  the 
presence  of  a  conductor  on  the  exterior  of  the  tube,  retreating 
from  the  side  where  it  is  touched.  This  sensitive  state  appears 
to  be  due  to  a  periodic  intermittence  in  the  discharge  j  an  inter- 
mittence or  partial  intermittence  in  the  flow  would  also  probably 
account  for  the  production  of  striae. 

295.  Electric  Oscillations. — Feddersen  examined 
the  spark  of  a  Leyden  jar  by  means  of  a  rotating  mirror, 
and  found  that  instead  of  being  a  single  instantaneous 
discharge,    it    exhibited l   certain    definite    fluctuations. 
With  very  small  resistances  in  the  circuit,  there  was  a  true 
oscillation  of  the  electricity  backward  and  forward  for 
a  brief  time,   these  alternate  partial  discharges  being 
probably  due  to  the  self-induction  of  the  circuit.     With 
a  certain  higher  resistance  the  discharge  became  con- 
tinuous  but   not   instantaneous.     With   a   still   higher 
resistance,  the  discharge  consisted  of  a  series  of  partial 
intermittent   discharges,    following    one  another  in   the 
same  direction.     Such  sparks  when  viewed  in  the  rotating 
mirror  showed  a  series  of  separate  images  at  nearly 
equal  distances  apart.      The  period  of  the  oscillations 
was  found  to  be  proportional  to  the  square  root  of  the 
capacity  of  the  condenser. 

296.  Velocity  of  Propagation  of  Discharge.— 
The  earliest  use  of  the  rotating  mirror  to  analyse  phe- 
nomena  of  short  duration  was  made  by  Wheatstone, 
who  attempted  by  this  means  to  measure  "  the  velocity 
of  electricity  "  in  conducting  wires.     What  he  succeeded 
in  measuring  was  not,  however,  the  velocity  of  electricity, 
but  the  time  taken  by  a  certain  quantity  of  electricity 
to  flow  through  a  conductor  of  considerable  resistance 
and  capacity.     Viewed,  in  a  rotating  mirror,  a  spark  of 

1  This  phenomenon  of  oscillation  vtzs  predicted  from  purely  tlicorelical  con 
t-:^.^.,t;r,n<5.  arising  out  of  the  equations  of  self-induction,  by  Sir  W.  Thomson 


CHAP.  iv.J    ELECTR1C1TV  AND  MAGNETISM.  249 

definite  duration  would  appear  to  be  drawn  out  into  an 
elongated  streak.  Such  an  elongation  was  found  to  be 
visible  v/hen  a  Leyden  jar  was  discharged  through  a 
copper  wire  half  a  mile  long ;  and  when  the  circuit  was 
interrupted  at  three  points,  one  in  the  middle  and  one  at 
each  end  of  this  wire,  three  sparks  were  obtained,  which, 
viev/ed  in  the  mirror,  showed  a  lateral  displacement, 
indicating  (with  the  particular  rate  of  rotation  employed) 
that  the  middle  spark  took  place  ^—^  of  a  second 
later  than  those  at  the  ends.  Wheatstone  argued  from  this 
a, velocity  of  288,000  miles  per  second.  But  Faraday 
showed  that  the  apparent  rate  of  propagation  of  a 
quantity  of  electricity  must  be  affected  by  the  capacity 
of  the  conductor ;  and  he  even  predicted  that  since  a 
submerged  insulated  cable  acts  like  a  Leyden  jar  (see 
Art.  274),  and  has  to  be  charged  before  the  potential 
at  the  distant  end  can  rise,  it  retards  the  apparent  flow 
of  electricity  through  it.  Professor  Fleeming  Jenkin 
says  of  one  of  the  Atlantic  cables,  that,  after  contact 
with  the  battery  is  made  at  one  end,  no  effect  can  be 
detected  at  the  other  for  two -tenths  of  a  second,  and 
that  then  the  received  current  gradually  increases,  until 
about  three  seconds  afterwards  it  reaches  its  maximum, 
and  then  dies  away.  This  retardation  is  proportional 
to  the  square  of  the  length  of  the  cable  as  well  as  to 
its  capacity  and  to  its  resistance ;  hence  it  becomes 
very  serious  on  long  cables,  as  it  reduces  the  speed 
of  signalling.  There  is  in  fact  no  definite  assignable 
"  velocity  of  electricity." 

A  very  simple  experiment  will  enable  the  student  to 
realise  the  excessively  short  duration  of  the  spark  of  a 
Leyden  jar.  Let  a  round  disc  of  cardboard  painted 
with  black  and  white  sectors  be  rotated  very  rapidly  so 
as  to  look  by  ordinary  light  like  a  mere  gray  surface. 
When  this  is  illuminated  by  the  spark  of  a  Leyden  jar  it 
appears  to  be  standing  absolutely  still,  however  rapidly 
it  may  be  turning.  A  flash  of  lightning  is  equally  in- 


250 


ELEMENTARY  LESSONS  ON       [CHAP.  IV. 


stantaneous :   it    is   utterly  impossible  to  determine  at 
which  end  the  flash  begins.1 

297.  Electric  Dust-figures. — Electricity  may  creep 
slowly  over  the  surface  of  bad  conductors.  Lichtenberg 
devised  an  ingenious  way  of  investigating  the  distribution 
of  electricity  by  means  of  certain  dust -figures.  The 
experiment  is  very  easy.  Take  a  charged  Leyden  jar 
and  write  with  the  knob  of  it  upon  a  cake  of  shellac 
or  a  dry  sheet  of 'glass.  Then  sift,  through  a  bit  of 


Fig.  109.. 

muslin,  over  the  cake  of  shellac  a  mixture  of  powdered 
red  lead  and  sulphur  (vermilion  and  lycopodium  powder 
answer  equally  well).  The  powders  in  this  process  rub 
against  one  another,  the  red  lead  becoming  +,  the 
sulphur  - .  Hence  the  sulphur  will  be  attracted  to 
those  parts  where  there  is  +  electrification  on  the  disc, 
and  settles  down  in  curious  branching  yellow  streaks  like 

1  Sometimes  the  flash  seems  to  strike  downwards  from  the  clouds  some- 
times upwards  from  the  earth.  This  is  an  optical  illusion,  resulting  from  the 
unequal  sensitiveness  to  light  of  different  portions  of  the  retina  of  the  eye. 


CHAP,  iv.]    ELECTRICITY  AND  MAGNETISM. 


251 


those  shown  in  Fig.  109.  The  red  lead  settles  down  in 
little  red  heaps  and  patches  where  the  electrification  is 
negative.  Fig.  no  shows  the  general  appearance  of 
the  Lichtenberg1  s  figure  produced  by  holding  the  knob  of 


Fig.  no. 

the  Leyden  jar  at  the  centre  of  a  shellac  plate  that  has 
previously  been  rubbed  with  flannel,  the  negative  elec- 
trification being  attracted  upon  all  sides  toward  the 
central  positive  charge. 

Powdered  tourmaline,  warmed  and  then  sifted  over  a 
sheet  of  glass  previously  electrified  irregularly,  will  show 
similar  figures,  though  not  so  well  defined. 

Breath-figures  can  be  made  by  electrifying  a  coin  or 
other  piece  of  metal  laid  upon  a  sheet  of  dry  glass, 
and  then  breathing  upon  the  glass  where  the  coin  lay, 
revealing  a  faint  image  of  it  on  the  surface  of  the  glass. 

298.  Production  of  Ozone. — Whenever  an  elec- 
tric machine  is  worked  a  peculiar  odour  is  perceived. 
[This  was  formerly  thought  to  be  evidence  ofjth'e  existence. 


252  ELEMENTARY  LESSONS  ON       [CHAP,  iv 

of  an  electric  "effluvium"  or  fluid;  it  is  now  known  to  be 
due  to  the  presence  of  ozone,  a  modified  form  of  oxygen 
gas.  which  differs  from  oxygen  in  being  denser,  more 
active  chemically,,  and  in  having  a  characteristic  smell. 
The  discharge  cf  the  Holtz-machine  and  that  of  the 
induction  coil  are  particularly  favourable  to  the  pro- 
duction of  this  substance. 

299.  Dissipation  of  Charge. — However  well  in- 
sulated a  charged  conductor  may  be,  and  however  dry 
the  surrounding  air,  it  nevertheless  slowly  loses  its 
charge,  and  in  a  few  days  will  be  found  to  be  completely 
discharged.  The  rate  of  loss  of  charge  is,  however,  not 
uniform.  It  is  approximately  proportional  to  the  dif- 
ference of  potential  between  the  body  and  the  earth. 
Hence  the  rate  of  loss  is  greater  at  first  than  afterwards, 
and  is  greater  for  highly  charged  bodies  than  for  those 
feebly  charged.  The  law  of  dissipation  of  charge 
therefore  resembles  Newton's  law  of  cooling,  according 
to  which  the  rate  of  cooling  of  a  hot  body  is  propor- 
tional to  the  difference  of  temperature  between  it  and 
the  surrounding  objects.'  If  the  potential  of  the  body 
be  measured  at  equal  intervals  of  time  it  will  be  found 
to  have  diminished  in  a  decreasing  geometric  series ;  or 
the  logarithms  of  the  potentials  at  equal  intervals  of  time 
will  differ  by  equal  amounts. 

This  may  be  represented  by  the  following  equation  : 

V*    —  V  f  -** 
vt  -    *  o  e        > 

where  V0  represents  the  original  potential  and  Vt  the  potential 
after  an  interval  /.  Here  e  stands  for  the  number  271828  .  .  . 
(the  base  of  the  natural  logarithms),  and  p  stands  for  the  "co- 
efficient of  leakage,"  which  depends  upon* the  temperature, 
pressure,  and  humidity  of  the  air. 

The  rate  of  loss  is,  however,  greater  at  negatively 
electrified  surfaces  than  at  positive. 

COO.  Positive  and  Negative  Electrification 

The  student  will  not  have  failed  to  notice  throughout 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  253 

this  Lesson  frequent  differences  between  the  behaviour 
of  positive  and  negative  electrification.  The  striking  dis- 
similarity in  the  Lichtenberg's  figures,  the  displacement 
of  the  perforation  -  point  in  Lullin's  experiment,  the 
unequal  tendency  to  dissipation  at  surfaces,  the  remark- 
able differences  in  the  various  forms  of  brush  and  glow 
discharge,  are  all  points  that  claim  attention.  Gassiot 
described  the  appearance  in  vacuum  tubes  as  of  a  force 
emanating  from  the  negative  pole.  Crookes's  experi- 
ments in  high  vacua  show  molecules  to  be  violently 
discharged  from  the  negative  electrode,  the  vanes  of  a 
little  fly  enclosed  in  such  tubes  being  moved  from  the 
side  struck  by  the  negative  discharge.  Holtz  found  that 
when  funnel-like  partitions  were  fixed  in  a  vacuum  tube 
the  resistance  is  much  less  when  the  open  mouths  of  the 
funnels  face  the  negative  electrode.  These  matters  are 
yet  quite  unaccounted  for  by  any  existing  theory  of 
electricity. 

The  author  of  these  Lessons  is  disposed  to  take  the  following  view  on  tnis 
point : — If  electricity  be  really  one  and  not  two,  efther  the  so-called  positive 
or  the  negative  electrification  must  be  a  state  in  v>  hich  there  is  tnote  electricity 
than  in  the  surrounding  space,  and  the  other  must  be  a  state  in  which  there 
is  less.  The  student  was  tcld,  in  Art.  6,  that  in  the  present  state  of  the  science 
we  do  not  know  for  certain  whether  "positive"  electrification  is  really  an 
excess  of  electricity  or  a  defect.  Now  some  of  the  phenomena  alluded  to  in 
this  Article  seem  to  indicate  that  the  so-called  "negative"  electrification 
really  is  the  state  of  excess.  In  particular,  the  fact  that  the  rate  of  dissipa- 
tion of  charge  is  greater  for  negative  electrification  than  for  positive,  points 
this  way ;  because  the  law  of  loss  of  charge  is  the  exact  counterpart  of  the 
law  of  the  loss  of  heat,  in  which  it  is  quite  certain  that,  for  equal  differences 
of  temperature  between  a  body  and  its  surroundings,  the  rate  of  loss  of  heat 
is  greater  at  higher  temperatures  than  at  lower ;  or  the  body  that  is  really 
hotter  loses  its  heat  fastest. 


LESSON  XXIV. — Atmospheric  EledriMy. 

SOL  The  phenomena  of  atmospheric  electricity  are 
of  two  kinds.  There  are  the  well-known  electrical  pheno- 
mena of  thunderstorms ;  and  there  are  the  phenomena 


254  ELEMENTARY  LESSONS  ON       [CHAP.  rv. 

of  continual  slight  electrification  in  the  air,  best  observed 
when  the  weather  is  fine.  The  phenomena  of  the  Aurora 
constitute  a  third  branch  of  the  subject. 

302.  The  Thunderstorm  an  Electrical  Pheno- 
menon.—  The  detonating  sparks  drawn  fr«m  electrical 
machines  and  from  Leyden  jars  did  not  fail  to  suggest 
to  the  early  experimenters,  Hawkesbee,  Newton,  Wall, 
Nollet,  and  Gray,  that  the  lightning  flash  and  the  thunder- 
clap were  due  to  electric  discharges.-  In  1749,  Ben- 
jamin Franklin,  observing  lightning  to  possess  almost 
all  the  properties  observable  in  electric  sparks,1  suggested 
that  the  electric  action  of  points  (Art.  43),  which  was 
discovered  by  him,  might  be  tried  on  thunderclouds, 
and  so  draw  from  them  a  charge  of  electricity.  He 
proposed,  therefore,  to  fix  a  pointed  iron  rod  to  a  high 
tower.  Before  he  could  carry  his  proposal  into  effect, 
Dalibard,at  Marly-la-ville,near  Paris,  taking  up  Franklin's 
hint,  erected  an  iron  rod  40  feet  high,  by  which,  in  1752, 
he  succeeded  in  drawing  sparks  from  a  passing  cloud. 
Franklin  shortly  after  succeeded  in  another  way.  He 
sent  up  a  kite  during  the  passing  of  a  storm,  and  found 
the  wetted  string  to  conduct  electricity  to  the  earth,  and 
to  yield  abundance  of  sparks.  These  he  drew  from  a 
key  tied  to  the  string,  a  silk  ribbon  being  interposed 
between  his  hand  and  the  key  for  safety.  Leyden  Jars 
could  be  charged,  and  all  other  electrical  effects  pro- 
duced, by  the  sparks  furnished  from  the  clouds.  The 
proof  of  the  identity  was  complete.  The  kite  experi- 
ment was  repeated  by  Romas,  who  drew  from  a  metallic 

1  Franklin  enumerates  specifically  an  agreement  between  electricity  and' 
lightning  in  the  following  respects : — Giving  light ;  colour  of  the  light ; 
crooked  direction ;  swift  motion ;  being  conducted  by  metals ;  noise  in 
exploding ;  conductivity  in  water  and  ice ;  rending  imperfect  conductors ; 
destroying  animals  ;  melting  metals ;  firing  inflammable  substances ;  sul- 
phureous smell  (due  to  ozone,  as  we  now  know) ;  and  he  had  previously  found 
that  needles  could  be  magnetised^both  by  lightning  anrrty  the  electric  spark. 
He  also  drew  attention  to  the  similarity  between  the  pale-blue  flame  seen 
during  thundery  weather  playing  at  the  tips  of  the  masts  of  ships  (called  by 
sailors  St.  ELrao'a  Fire),  and  the  "glow"  discharge  at  points. 


CHAP,  iv.}    ELECTRICITY  AND  MAGNETISM.  2^5 

string  sparks  9  feet  long,  and  by  Cavallo,  who  made 
many  important  observations  on  atmospheric  electricity. 
In  1753  Richmann,  of  St.  Petersburg,  who  was  experi- 
menting with  an  apparatus  resembling  that  of  Dalibard, 
vas  struck  by  a  sudden  discharge  and  killed. 

303.  Theory  of  Thunderstorms.  —  Solids  and 
liquids  cannot  be  charged  throughout  their  substance ; 
if  charged  at  all  the  electricity  is  upon  their  surface  (see 
Art.  29).  But  gases  and  vapours,  being  composed  of 
myriads  of  separate  particles,  can  receive  a  bodily  charge. 
The  air  in  a  room  in  which  an  electric  machine  is 
worked  is  found  afterwards  to  be  charged.  The  clouds 
are  usually  charged  more  or  less  with  electricity,  derived, 
probably,  from  evaporation 1  going  on  at  the  earth's 
surface.  The  minute  particles  of  water  floating  in  the 
air  being  belter  conductors  than  the  air  itself  become 
more  highly  charged.  As  they  fall  by  gravitation  and 
unite  together,  the  strength  of  their  charges  increases. 
Suppose  eight  small  drops  to  join  into  one.  That  one 
will  have  eight  times  the  quantity  of  electricity  dis- 
tributed over  the  surface  of  a  single  sphere  of  twice  the 
radius  (and,  therefore,  of  twice  the  capacity,  by  Art.  247) 
of  the  original  drops  ;  and  its  electrical  potential  will 
therefore  be  four  times  as  great.  Now  a  mass  of  cloud 
may  consist  of  such  charged  spheroids,  and  its  potential 
may  gradually  rise,  therefore,  by  the  coalescence  of  the 
drops,  and  the  electrification  at  the  lower  surface  of  the 
cloud  will  become  greater  and  greater,  the  surface  of  the 
earth  beneath  acting  as  a  condensing  plate  and  becom- 
ing inductively  charged  with  the  opposite  kind  of  elec- 
trification. Presently  the  difference  of  potential  becomes 
so  great  that  the  intervening  strata  of  air  give  way  under 
the  strain,  and  a  disruptive  discharge  takes  place  at  the 
point  where  the  air  offers  least  resistance.  This  light- 
ning spark,  which  may  be  more  than  a  mile  in  length, 
discharges  only  the  electricity  that  has  been  accumulat- 

1  Sec  Art.  63. 


256  ELEMENTARY  LESSONS  ON       [CHAP.  iv. 


ing  at  the  surface  of  the  cloud,  and  the  other  parts  of 
the  cloud  will  now  react  upon  the  discharged  portion, 
producing  internal  attractions  and  internal  discharges. 
The  internal  actions  thus  set  up  will  account  for  tha 
usual  appearance  of  a  thundercloud,  that  it  is  a  well- 
defined  flat-bottomed  mass  of  cloud  which  appears  at  the 
top  to  be  boiling  or  heaving  up  with  continual  move- 
ments. 

3O4.  Lightning  and  Thunder. — Three  kinds  of 
lightning  have  been  distinguished  by  Arago  :  (i.)  The 
Zig-zag  flash  or  "  Forked  lightning"  of  ordinary  occur- 
rence. The  zig-zag  form  is  probably  due  either  to  the 
presence  of  solid  particles  jn  the  air  or  to  local  electrifi- 
cation at  certain  points,  making  the  crooked  path 'the 
one  of  least  resistance,  (ii.)  Sheet  lightning,  in  which 
whole  surfaces  are  lit  up  at  once,  is  probably  only  the 
reflection  on  the  clouds  of  a  flash  taking  place  at  some 
other  part  of  the  sky.  It  is  often  seen  on  the  horizon  at 
night,  reflected  from  a  storm  too  far  away  to  produce 
audible  thunder,  and  is  then  known  as  "  summer  light- 
ning." (iii.)  Globular  lightning,  in  the  form  of  balls  oj 
fire,  which  move  slowly  along  and  then  burst  with  a 
sudden  explosion.  This  form  is  very  raie,  but  must  be 
admitted  as  a  real  phenomenon,  though  some  of  the 
accounts  of  it  are  greatly  exaggerated.  Similar  phe- 
nomena on  a  small  scale  have  been  produced  (though 
usually  accidentally)  with  electrical  apparatus.  Cavallo 
gives  an  account  of  a  fireball  slowly  creeping  up  the 
brass  wire  of  a  large  highly  charged  Leyden  jar,  and 
then  exploding  as  it  descended ;  and  Plantc*  has  recently 
observed  similar  but  smaller  globular  discharges  from 
his  "rheostatic  machine"  charged  by  powerful  second- 
ary batteries. 

The  sound  of  the  thunder  may  vary  with  the  con- 
ditions of  the  lightning  spark.  The  spark  heats  the  air 
in  its  path,  causing  sudden  expansion  and  compression 
all  round,  followed  by  as  sudden  a  rush  of  air  into  the 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM.  557 

partial  vacuum  thus  produced  If  the  spark  be  straight 
and  short,  the  observer  will  hear  but  one  short  sharp  clap. 
If  its  path  be  a  long  one  and  not  straight,  he  will  hear 
the  successive  sounds  one  after  the  other,  with  a  charac- 
teristic rattle^  and  the  echoes  from  other  clouds  will 
come  rolling  in  long  afterwards.  The  lightning -flash 
itself  never  lasts  more  than  100*000  °f  a  second. 

The  damage  done  by  a  lightning-flash  when  it  strikes 
an  imperfect  conductor  appears  sometimes  as  a  disrup- 
tive mechanical'  disintegration,  as  when  the  masonry 
of  a  chimney-stack  or  church-spire  is  overthrown,  and 
sometimes  as  an  effect  of  heat,  as  when  bell- wires  and 
objects  of  metal  in  the  path  of  the  lightning-current  are 
fused.  The  physiological  effects  of  sudden  discharges 
are  discussed  in  Art. -226.  The  remedy  against  disaster 
by  lightning  is  to  provide  an  efficient  conductor  com- 
municating with  a  conducting  stratum  in  the  earth. 

The  "  return-stroke "  experienced  by  persons  in  the 
neighbourhood  of  a  flash  is  explained  in  Art.  26. 

3O5.  Lightning  Conductors. — The  first  suggest- 
ion to  protect  property  from  destruction  by  lightning 
was  made  by  Franklin  in  1749,  in  the  following  words  : 

"  May  not  the  knowledge  of  this  power  of  points  be  of  use 
to  mankind,  in  preserving  houses,  churches,  ships,  etc.,  from 
the  stroke  of  lightning,  by  directing  us  to  fix  on  the  highest 
parts  of  those  edifices  upright  rods  of  iron  made  sharp  as  a 
needle,  and  gilt  to  prevent  rusting,  and  from  the  foot  of  those 
rods  a  wire  down  the  outside  of  the  building  into  the  ground, 
or  round  one  of  the  shrouds  of  a  ship,  and  down  her  side  till 
it  reaches  the  water  ?  Would  not  these  pointed  rods  probably 
draw  the  electrical  fire  silently  out  of  a  cloud  before  it  came 
riigh  enough  to  strike,  and  thereby  secure  us  from  that  most 
sudden  a;:d  terrible  mischief." 

The  four  essential  points  of  a  good  lightning-conductor 
are — (i)  that  its  apex  be  a  fine  point  elevated  above  the 
highest  point  of  the  building  ;  (2)  that  its  lower  end  passes 
either  into  a  stream  or  into  wet  straUm  of  ground  ;  (3) 

s 


258  ELEMENTARY  LESSONS  ON       [CHAP.  IV." 

that  the  conductor  between  the  apex  and  the  ground  be 
perfectly  continuous  and  of  sufficient  conducting  power ; 
(4)  that  the  leads  and  any  iron  work  or  metal  work  about 
the  roofs  or  chimneys  be  connected  by  stout  wires  with 
the  main  conductor.  Too  great  importance  cannot  be 
attached  to  the  second  and  third  of  these  essentials. 
Maxwell  has  proposed  to  cover  houses  with  a  network 
of  conducting  wires,  without  any  main  conductor,  the 
idea  being  that  then  the  interior  of  the  building  will, 
like  Faraday's  hollow  cube  (Art.  31),  be  completely  pro- 
tected from  electric  force.  Much  controversy  has  arisen 
of  late  respecting  lightning-rods,  Professor  Oliver  Lodge 
maintaining  that  a  lightning  flash  to  be  of  the  nature  of 
an  electric  oscillation  (Art.  295)  rather  than  a  current. 
If  so,  the  conductor  of  least  resistance  is  not  necessarily 
the  best  lightning-rod.  Professor  Lodge  and  the  author 
independently,  and  for  different  reasons,  recommend  iron 
in  preference  to  copper  for  lightning-rods. 

3O6.  Atmospheric  Electricity.  —  In  1752  Le- 
monnier  observed  that  the  atmosphere  usually  was  in 
an  electrical  condition.  Cavallo,  Beccaria,  Ceca,  and 
others,  added  to  our  knowledge  of  the  subject,  and 
more  recently  Quetelet  and  Sir  W.  Thomson  have 
generalised  from  more  careful  observations.  The  main 
result  is  that  the  air  above  the  surface  of  the  earth  is 
usually,  during  fine  weather,  positively  electrified,  or  at 
least  that  it  is  positive  with  respect  to  the  earth's 
surface,  the  earth's  surface  being  relatively  negative. 
The  so-called  measurements  of  "  atmospheric  electricity  " 
are  really  measurements  of  difference  of  potential  between 
a  point  of  the  earth's  surface,  and  a  point  somewhere  in 
the  air  above  it.  In  the  upper  regions  of  the  atmosphere 
the  air  is  highly  rarefied,  and  conducts  electricity  as  do 
the  rarefied  gases  in  Geissler's  tubes  (Art.  292).  The 
lower  air  is,  when  dry,  a  non-conductor.  The  upper 
stratum  is  believed  to  be  charged  with  +  electricity, 
while  the  earth's  surface  is  itself  negatively  charged  ; 


CHAP.  iv.J    ELECTRICITY  AND  MAGNETISM.  25$ 

the  stratum  of  denser  air  between  acting  like  the 
glass  of  a  Leyden  jar  in  keeping  the  opposite  charges 
separate.  If  we  could  measure  the  electric  potential  at 
different  points  within  the  thickness  of  the  glass  of  a 
Leydeh  jar,  we  should  find  that  the  values  of  the 
potential  changed  in  regular  order  from  a  +  value  at 
one  side  to  a  —  value  at  the  other,  there  being  a  point 
of  zero  potential  about  half  way  between  the  two.  Now, 
the  air  in  fine  weather  always  gives  +  indications,  and 
the  potential  of  it  is  higher  the  higher  we  go  to 
measure  it.  Gavallo  found  more  electricity  in  the  air 
just  outside  the  cupola  of  St.  Paul's  Cathedral  than 
at  a  lower  point  of  the  building.  Sir  W.  Thomson 
found  the  potential  in  the  island  of  Arran  to  increase 
from  23  to  46  volts  for  a  rise  of  one  foot  in  level ;  but 
the  difference  of  potential  was  sometimes  eight  or  ten 
times  as  much  for  the  same  difference  of  level,  and 
changed  rapidly,  as  the  east  wind  blew  masses  of  cloud 
charged  with  +  or  —  electricity  across  the  sky.  Joule 
and  Thomson,  at  Aberdeen,  found  the  rise  of  potential 
to  be  equal  to  40  volts  per  foot,  or  i  -3  volts  per  centi- 
metre rise  of  level 

During  fine  weather  a  negative  electrification  of  the 
air  is  extremely  rare.  Beccaria  only  observed  it  six 
times  in  fifteen  years,  and  then  with  accompanying 
winds.  But  in  broken  weather  and  during  rain  it  is 
more  often  —  than  +,  and  exhibits  great  fluctuations, 
changing  from  -  to  + ,  and  back,  several  times  in  half 
an  hour.  A  definite  change  in  the  electrical  conditions 
usually  accompanies  a  change  of  weather.  "  If,  when 
the  rain  has  ceased  (said  Ceca),  a  strong  excessive  (  + ) 
electricity  obtains,  it  is  a  sign  that  the  weather  wilJ 
continue  fair  for  several  days." 

307.  Methods  of  Observation.  —  The  older 
observers  were  content  to  affix  to  an  electroscope  (with 
gold  leaves  or  pith -bails)  an  insulated  pointed  rod 
stretching  out  into  the  air  above  the  ground,  or  to  fly  a 


alto  ELEMENTARY  LESSONS  ON       [CHAP,  iv 

kite,  or  (as  Becquerel  did)  to  shoot  into  the  air  an  arrow 
communicating  with  an  electroscope  by  a  fine  wire,  uhich 
was  removed  before  it  fell.  Gay  Lussac  and  Biot  lowered 
a  wire  from  a  balloon,  and  found  a  difference  of  potential 
between  the  upper  arid  lower  strata  of  the  air.  None 
of  these  methods  is  quite  satisfactory,  for  they  do  not 
indicate  the  potential  at  any  one  point.  To  bring  the 
tip  of  a  rod  to  the  same  potential  as  the  surrounding  air, 
it  is  necessary  that  material  particles  should  be  discharged 
from  that  point  for  a  short  time,  each  particle  as  it 
breaks  away  carrying  with  it  a  +  or  a  —  charge  until 
the  potentials  are  equalised  between  the  rod  and  the 
air  at  that  point.  Volta  did  this  by  means  of  a  small 
flame  at  the  end  of  an  exploring  rod.  Sir  W.  Thomson 
has  employed  a  *'  water -dropper,"  an  insulated  cistern 
provided  with  a  nozzle  protruding  into  the  air,  from 
which  drops  issue  to  equalise  the  potentials  :  in' winter 
he  uses  a  small  roll  of  smouldering  touch-paper.  Dell- 
mann  adopted  another  method,  exposing  a  sphere  to 
induction  by  the  air,  and  then  insulating  it,  and  bringing 
it  within  doors  to  examine  its  charge.  Peltier  adopted 
the  kindred  expedient  of  placing,  on  or  near  the  ground, 
an  electrometer  of  the  form  shown  in  Fig.  1 1 1 ,  which 
during  exposure  was  connected  to  the  ground,  then 
insulated,  then  removed  in-doors  for  examination.  This 
process  really  amounted  to  charging  the  electrometer 
by  induction  with  electricity  of  opposite  sign  to.  that  of 
the  air.  The  principle  of  this  particular  electrometer 
was  explained  in  Art.  260.  Of  recent  years  the  more 
exact  electrometers  of  Sir  W.  Thomson,  particularly  the 
"  quadrant "  electrometer,  described  in  Art.  262,  the 
"  divided-ring  "  electrometer,  and  a  "  portable  "  electro- 
meter on  the  same  general  principle,  have  been  used 
for  observations  on  atmospheric  electricity.  These 
electrometers  have  the  double  advantage  of  giving 
quantitative  readings,  and  of  being  readily  adapted  to 
automatic  registration,  by  recording  photographically  the 


CHAP,  iv.]   ELECTRICITY  AND  MAGNETISM. 


261 


movements  of  a  spot  of  light  reflected  from  a  small 
mirror  attached  to  their  needle.  Using  a  water-dropping 
collector  and  a  Thomson  electrometer,  Everett  made 


Fig.  in. 

a  series  of  observations  in  Nova  Sctotia,  and  found  the 
highest  +  electrification  in  frosty  weather,  with  a  dry 
wind  charged  with  particles  of  ice. 

308.  Diurnal  Variations. — Quetelet  found  that  at 
Brussels  the  daily  indications  (during  fine  weather) 
showed  two  maxima  occurring  in  summer  at  8  a.m.  and 
9  p.m.,  and  in  winter  at  10  a.m.  and  6  p.m.  respectively, 


262  ELEMENTARY  LESSONS  ON      {CHAP.  TV. 

and  two  minima  which  in  summer  were  at  the  hours  ol 
Ifp.m.  and  about  midnight.  He  also  found  that  in  January 
the  electricity  was  about  thirteen  times  as  strong  as  in 
June.  Observations  made  by  Prof.  B.  Stewart  at  Kew 
show  a  maximum  at  8  a.m.  in  summer  at  10  a.m.  in 
winter,  and  a  second  minimum  at  I  o  p.m.  in  summer 
and  7  p.m.  in  winter.  The  maxima  correspond  fairly 
with  hours  of  changing  temperature,  the  minima  with 
those  of  constant  temperature.  In  Paris,  M.  Mascart 
finds  but  one  maximum  just  before  midnight :  at  sun- 
rise the  electricity  diminishes  until  about  3  p.m.,  when  it 
has  reached  a  minimum,  whence  it  rises  till  nightfall. 

Our  knowledge  of  this  important  subject  is  still  very 
imperfect.  We  do  not  even  know  whether  all  the 
changes  of  the  earth's  electrification  relatively  to  the  air 
are  due  to  causes  operating  above  or  below  the  earth's 
surface.  Simultaneous  observations  at  different  places 
and  at  different  levels  are  greatly  wanted. 

3O9.  The  Aurora. — In  all  the  northern  regions  ol 
the  earth  the  Aurora  borealis,  or  "  Northern  Lights,"  is 
an  occasional  phenomenon  ;  and  within  and  near  the 
Arctic  circle  is  of  almost  nightly  occurrence.  Similar 
lights  are  seen  in  the  south  polar  regions  of  the  earth, 
and  are  denominated  Aurora  australis.  .As  seen  in 
European  latitudes,  the  usual  form  assumed  by  the 
aurora  is  that  of  a  number  of  ill-defined  streaks  or 
streamers  of  a  pale  tint  (sometimes  tinged  with  red  and 
other  colours),  either  radiating  in  a  fan -like  form  from 
the  horizon  in  the  direction  of  the  (magnetic)  north,  or 
forming  a  sjort  of  arch  across  that  region  of  the  sky,  of 
the  general  form  shown  in  Fig.  112.  A  certain  flicker- 
ing or  streaming  motion  is  often  discernible  in  the 
streaks.  Under  very  favourable  circumstances  the 
aurora  extends  over  the  entire  sky.  The  appearance  of 
an  aurora  is  usually  acc.ompanied  by  a  magnetic  storm 
(Art.  145),  affecting  the  compass -needles  over  whole 
regions  of  the  globe.  This  fact,  and  the  position  of  the 


CHAP,  tv.]    ELECTRICITY  AND  MAGNETISM. 


263 


auroral  arches'  and  streamers  with  respect  to  the 
magnetic  meridian,  directly  suggest  an  electric  origin 
for  the  light, — a  conjecture  which  is  confirmed  by  the 
many  analogies  found  between  auroral  phenomena  and 


,Fig.  112. 

those  of  discharge  in  rarefied  air  (Arts.  292  and  294). 
Yet  the  presence  of  an  aurora  does  not,  at  least  in  our 
latitudes,  affect  the  electrical  conditions  of  the  lower 
regions  of  the  atmosphere.  On  September  i,  1859,  a 
severe  magnetic  storm  occurred,  and  auroras  were 
observed  almost  all-over  the  globe;  at  the  same  time 
a  remarkable  outburst  of  energy  took  place  in  the 
photosphere  of  the  sun  ;  but  'no  simultaneous  develop- 
ment of  atmospheric  electricity  was  recorded.  Auroras 
appear  in  greater_frequency  in  periods  of  about  n£ 


ELEMENTARY  LESSONS  ON       [CHAP.  iv. 


years,  which  agrees  pretty  well  with  the  cycles  of 
maximum  of  magnetic  storms  (see  Art  144)  and  of 
sun-spots. 

The  spectroscope  shows  the  auroral  light  to  be  due 
to  gaseous  matter,  its  spectrum  consisting  of  a  few 
bright  lines  not  referable  with  certainty  to  any  known 
terrestrial  substance,  but  having  a  general  resemblance 
to  those  seen  in  the  spectrum  of  the  electric  discharge 
through  rarefied  dry  air. 

The  most  probable  theory  of  the  aurora  is  that  origin- 
ally due  to  Franklin,  namely,  that  it  is  due  to  electric 
discharges  in  the  upper  air,  in  consequence  of  the  differ- 
ing electrical  conditions  between  the  cold  air  of  the  polar 
regions  and  the  warmer  streams  of  air  and  vapour  raised 
from  the  level  of  the  ocean  in  tropical  regions  by  the 
heat  of  the  sun.  For  evaporation  of  water  containing 
saline  matter  is  a  source  of  electrification  (see  Art.  63), 
the  escaping  vapour  becoming  positively  electrified. 

According  to  Nordenskiold  the  terrestrial  globe  is 
perpetually  surrounded  at  the  poles  with  a  ring  or  crown 
of  light,  single  or  double,  to  which  he  gives  the  name  of 
the  "  aurora-glory."  The  outer  edge  of  this  ring  he  esti- 
mates to  be  at  1 20  miles  above  the  earth's  surface,  and 
its  diameter  about  1250  miles.  The  centre  of  the  aurora- 
glory  is  not  quite  at  the  magnetic  pole,  being  in  iat. 
81°  NM  long.  80°  E.  This  aurora -glory  usually  appears 
as  a  pale  arc  of  light  across  the  sky,  and  is  destitute  of 
the  radiating  streaks  shewn  in  Fig.  112,  except  during 
magnetic  and  auroral  storms. 

An  artificial  aurora  has  been  produced  by  Lemstrbm, 
who  erected  on  a  mountain  in  Lapland  a  network  of 
wires  presenting  many  points  to  the  sky.  By  insulating 
this  apparatus  and  connecting  it  by  a  telegraph  wire 
with  a  galvanometer  at  the  bottom  of  the  mountain,  he 
was  able  to  observe  actual  currents  of  electricity  when 
the  auroral  beam  rose  above  the  mountain 


CHA?  v  ]    ELECTRICITY  AND  MAGNETISM.  265 


CHAPTER    V. 

ELECTROMAGNETICS. 

LESSON  XXV. — Theory  of  Magnetic  Potential. 

31O.  That  branch  of  the  science  of  electricity  which 
treats  of  the  relation  between  electric  currents  and  mag- 
netism is  termed  Electromagnetics.  In  Art.  1 1 7  the 
law  of  inverse  squares  as  applied  to  magnets  was  explained, 
and  the  definition  of  "unit  magnetic  pole"  was  given  in 
Art.  125.  The  student  also  learned  to  express  the  strength 
of  poles  of  magnets  in  terms  of  the  unit  pole,  and  to  apply 
the  law  to  the  measurement  of  magnetic  forces.  It  is, 
however,  much  more  convenient,  for  the  purpose  of  study, 
to  express  the  interaction  of  magnetic  and  electromagnetic 
systems  in  terms  not  of  "force"  but  of  *l  potential  n\ 
i.e.  in  terms  of  their  power  to  do  'work.  In  Art  237 
the  student  was  shown  how  the  electric  potential  4ue 
to  a  quantity  of  electricity  may  be  evaluated  -in  terms  of 
the  work  done  in  bringing  up  as  a  test  charge  a  unit  of 
-I-  electricity  from  an  infinite  distance.  Magnetic 
potential  can  be  measured  similarly  by  the  ideal  pro- 
cess of  bringing  up  a  unit  magnetic  pole  (N.- seeking) 
from  an  infinite  distance,  and  ascertaining  the  amount 
of  work  done  in  the  operation.  Hence  a  large  number 
of  the  points  proved  in  Lesson  XX.  concerning  electric 
potential  will  also,  hold  true  for  magnetic  potential.  The 
student  may  compare  the  following  propositions  with  the 
corresponding  ones  in  Articles  237  to  243: — 


266  ELEMENTARY  LESSONS  ON        [CHAP.  V. 

(a)  The  magnetic  potential  at  any  point  is  the  work 
that  must  be  spent  upon  a  unit  magnetic  (N. -seek- 
ing) pole  in  bringing  it  up  to  that  point  from  an 
infinite  distance. 

(b)  The  magnetic  potential  at  any  point  due  to   a 
system  of  magnetic  poles  is  the  sum  of  the  separate 
magnetic  potentials  due  to  the  separate  poles. 

The  student  must  here  remember  that  the  potentials  due 
to  S. -seeking  poles  will  be  of  opposite  sign  to-  those  due 
to  N. -seeking  poles,  and  must  be  reckoned  as  negative. 

(c)  The  (magnetic)  potential  at  any  point  due  to  a 
system  of  magnetic  poles  may  be  calculated  (com- 
pare with  Art.  238)  by  summing  up  the  strengths 
of  the    separate  poles  divided  each   by  its  own 
distance   from    that  point.      Thus,    if  poles   of 
strengths   ;;/',  /;/",  /«"',  etc.,   be    respectively  at 

distances  of  /,  /',  r"\ (centimetres) 

from  a  point  P,  then  the  following  equation  gives 
the  potential  at  P  : — 


.,         m 

p  =   r' 


(d)  The    difference   of  {magnetic}  potential  betiveen 
two  points  is  the  work  to  be  done  on  or  by  a 
unit  {N.-  seeking')  pole  in  moving  it  from  one 
point  to  the  other. 

(e)  Magnetic  force  is  the  rate  of  change  of  (magnetic) 
potential  per  unit  of  length. 

(f)  Equipotential  surfaces  are  those  (imaginary)  sur- 
faces surrounding  a  magnetic  pole  or  system   oj 
poles,    ovet   which   the   {magnetic)  potential   has 
equal  values.     Thus,  around  a  single  magnetic 
pole,  supposing  all  the  magnetism  to  be  collected 
at  a  point  far  removed  from  all  other  poles,  the 
potential    would    be    equal    all    round    at    equal 


CHAP,  v.]     ELECTRICITY  AND  MAGNETISM.  267 

distances  ;  and  the  equipotential  surfaces  would 
be  a  system  of  concentric  spheres  at  such  dis- 
tances apart  that  it  would  require  the  expendi- 
ture of  one  erg  of  work  to  move  a  unit  pole  up 
from  a  point  on  the  surface  of  one  sphere  to  any 
point  on  the  next  (see  Fig.  97).  Around  any  real 
magnet  possessing  two  polar  regions  the  equi- 
potential surfaces  would  be  much  more  com- 
plicated. Magnetic  force  ^  whether  of  attraction 
or  repulsion^  always  acts  across  the  equipotential 
surfaces  in  a  direction  normal  to  the  surface ;  the 
magnetic  lines  of  force  are  everywhere  perpen- 
dicular to  the  equipotential  surfaces. 

311.  Tubes  of  Force.  —  The  following  proposi- 
tion is  also  important : — From  a  single  magnetic  pole 
(supposed  to  be  a  point  far  removed  from  all  other 
poles)  the  lines  offeree  diverge  radially -in  all  directions. 
The  space  around  may  be  conceived  as  thus  divided  up 
into  a  number  of  conical  regions,  each  having  their  apex 
at  that  pole  ;  and  through  each  cone,  as  through  a  tube,  a 
certain  number  of  lines  of  force  will  pass.  Such  a  conical 
space  may  be  called  a  "tube  of  force."  No  matter 
where  you  cut  across  a  tube  of  force  the  cross-section 
will  cut  through  all  the  enclosed  lines  of  force,  though 
they  diverge  more  widely  as  the  tube  widens.  Hence, 
(g)  The  total  magnetic  force  exerted  across  any  section 

of  a  tube  of  force  is  constant  wherever  the  section 

be  taken. 

In  case  the  magnetism  is  not  concentrated  at  one 
point,  but  distributed  over  a  surface,  we  shall  have  to 
speak  of  the  "  amount  of  magnetism  "  rather  than  of  the 
"  strength  of  pole,"  and  in  such  a  case  the 

(h)  Afagnetic  density  is  the  amount  of  free  magnetism 
per  unit  of  surface.  In  the  case  of  a  simple 
magnetic  shell  over  the  face  of  which  the 
magnetism  is  distributed  with  uniform  density, 


268  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

the  "strength"  of  the  shell  will  be  equal  to  the  thick- 
ness of  the  shell  multiplied  by  the  surface-density. 

312.  Intensity  of  Field. — We  have  seen  (Art.  101,) 
that  every  magnet  is  surrounded  by  a  certain  "  field/5 
within  v/hich  magnetic   force  is  observable.     We  may 
completely   specify   the   properties  of  the   field   at   any 
point  by  measuring  the  strength  and  the  direction  of 
that  force, — that  is,   by  measuring  the  "intensity  of 
the  field"  and  the  direction  of  the  lines  of  force.      The 
"intensity  of  the  field r"  at  any  point  is  measured  by  the 

forte  with  whicli  it  ads  on  a  unit  magnetic  pole  placed 
at  that  point.  Hence,  unit  intensity  of  f,  eld  is  that 
intensity  of  field  which  acts  on  a  un~'t  pole  with  a  force 
of  one  dyne.  There  is  therefore  a  field  of  unit  intercity 
at  a  point  one  centimetre  distant  from  the  pole  of  a 
magnet  of  unit  strength.  Suppose  a  magnet  pole,  -./hose 
strength  is  m,  placed  in  a  field  at  a  point  where  the 
intensity  is  H,  then  the  force  v/ill  be  in  times  as  great 
as  if  the  pole  were  of  unit  strength,  and 

/=  m  x  H. 

We  may  also  take  as  a  measure  of  the  intensity  of 
the  field  at  any  point  the  number  of  lines  of  force  that 
pass  through  a  square  centimetre  of  surface  placed 
across  the  field  at  that  point.  //  follows  that  a  unit 
magnetic  pole  will  have  4?r  lines  of  force  proceeding  from 
it :  for  there  is  unit  field  at  unit  distance  av/ay,  or  one 
line  of  force  per  square  centimetre ;  and  there  are  4?r 
square  centimetres  of  surface  on  a  sphere  of  unit  radius 
drawn  round  the  pole.  A -magnet,  whose  pole-strength 
is  mt  has  ^m  lines  of  force  running  through  the  steel, 
and  diverging  at  its  pole. 

313.  Intensity    of  Magnetisation:    Magnetic 

Susceptibility    and    Magnetic     Permeability. 

When  a  piece  of  magnetic  metal  is  placed  in  a  magnetic 


CHAP,  v.]  ELECTRICITY  AND  MAGNETISM.  269 

field,  sjme  of  the  lines  of  magnetic  force  run  through  it 
and  magnetise  it.  The  intensity  of  its  magnetisation 
will  depend  upon  the  intensity  of  the  field  into  which  it 
is  put  and  upon  the  metal  itself.  There  are  two  ways 
of  looking  at  the  matter,  each  of  which  has  its  advant- 
ages. We  may  think  of  the  magnetism  of  the  iron  or 
other  metal  as  something  resident  on  the  polar  surfaces, 
and  expressed  therefore  in  units  of  magnetism :  or  we 
may  think  about  the  internal  condition  of  the  piece  of 
metal,  and  of  the  number  of  magnetic  lines  that  are 
running  through  it  and  emerging  from  it  into  the  sur- 
rounding space.  This  is  the  more  .modern  way.  The 
fact  that  soft  iron  placed  in  the  magnetic  field  becomes 
highly  magnetic  may  then  be  expressed  in  the  following 
two  ways  : — (i)  iron  when  placed  in  the  magnetic  field 
develops  strong  poles  on  its  end  surfaces,  being  highly 
susceptible  to  magnetisation  ;  (2)  when  iron  is  placed  in 
the  magnetic  field,  the  magnetic  lines  gather  themselves 
up  and  run  in  greater  quantities  through  the  space 
now  occupied  by  iron,  for  iron  is  very  permeable  to  the 
lines  of  magnetic  induction,  being  a  good  conductor  cf 
the  magnetic  lines.  Each  of  these  ideas  may  be 
rendered  exact  by  the  introduction  of  appropriate 
coefficients. 

The  coefficient  of  magnetisation,  or  suscepti- 
bility, is  based  on  unit  of  pole  strength.  Suppose  a 
magnet  to  have  tn  units  of  magnetism  on  each  pole ; 
then  if  the  length  between  its  poles  is  /,  the  product 
m  x  /  is  called  its  magnetic  moment,  and  the  magnetic 
moment  divided  by  its  volume  is  called  its  intensity  of 
magnetisation;  this  term  being  intended,  though  based 
on  surface-unit  of  pole  strength,  to  convey  an  idea  as  to 
the  internal  magnetic  state.  Seeing  that  volume  is  the 
product  of  sectional  area  into  length,  it  follows  that  if 
any  piece  of  iron  or  steel  of  uniform  section  had  its 
surface  magnetism  situated  on  its  ends  only,  its  intensity 
of  magnetisation  would  be  equal  to  the  strength  of  pole 


270  ELEMENTARY  LESSONS  ON        [CHAP.  V. 

divided  by  the  area  of  end  surface.     Writing  I  for  the 
intensity  of  magnetisation  we  should  have 

T   mag,  moment  *n  X  /  #* 

volume  s  X  /          s ' 

Now,  supposing  this  intensity  of  magnetisation  •  were 
due  to  the  iron  having  been  put  into  a  magnetic  field  of 
intensity  H,  we  find  that  the  ratio  between  the  resulting 
intensity  of  magnetisation  I  and  the  magnetising  force 
•H  producing  it  is  expressible  by  a  numerical  coefficient 
of  magnetisation,  or  susceptibility,  k<  We  may  write  : 

I  =£H 
or  ^  =  H 

This  may  be  looked  at  as  saying  that  for  every  mag- 
netic line  in  the  field  there  will  be  k  units  of  magnet- 
ism on  the  end  surface. 

In  magnetic  substances  such  as  iron,  steel,  nickel, 
etc.,  the  susceptibility  k  has  positive  values ;  but  there 
are  many  substances  such  as  bismuth,  copper,  mercury, 
etc.,  which  possess  feeble  negative  coefficients.  These 
latter  are  termed  "  diamagnetic  "  bodies  (Art.  339)  and 
are  repelled  by  the  poles  of  magnets.  The  values  of  k 
vary  very  much'  in  iron,  not  only  in  the  different  qualities 
of  iron,  but  vary  in  every  specimen  with  the  stage  of 
magnetisation. ,  When  a  piece  of  iron  has  become  well 
magnetised  it  is  no  longer  as  susceptible  to  magnetisa- 
tion as  it  was  at  first :  it  is  becoming  "  saturated." 
Barlow  found  the  value  of  k  for  iron  to  be  32-8,  Thalen 
found  it  from  32  to  44,  Archibald  Smith  80  to  90, 
Stoletow  21  to  174;  Rowland  found  Norwegian  iron  to 
go  as  high  as  366  ;  Ewing  found  thin  soft  iron  wires  go 
up  to  1300  or  1400.  Stoletow  showed  that  iron  in  a 
weak  magnetic  field  showed  a  small  susceptibility,  which 
greatly  increased  as  the  magnetising  force  in  the  field 
was  strengthened,  but  again  fell  off  with  still  greater 
forces  as  the  iron  got  saturated.  When  very  intense 


CHAP,  v.]  ELECTRICITY  AND  MAGNETISM.  271 

magnetising  forces  are  used,  so  that  the  intensity  of 
magnetisation  is  very  great,  the  susceptibility  (and  per- 
meability) is  practically  reduced  to  zero.  It  appears 
that  the  maximum  intensity  of  magnetisation  that  can 
be  given  to  i*on  and  steel  is  about  1 500  (units,  per 
square  centimetre  of  cross  section).  According  to 
Rowland  the  maximum  for  cobalt  is  800,  for  nickel 
494.  Steel  does  not  retain  all  the  magnetisation  that 
can  be  temporarily  induced  in  it,  its  maximum  intensity 
being,  according  to  Weber  400,  according  to  Von 
Waltenhofen  470,  according  to  Rowland  785,  accord- 
ing to  Hopkinson  878.  Everett  has  calculated  (from 
Gauss's  observations)  that  the  intensity  of  magnetisation 
of  the  earth  is  only  0-0790,  or  only  TY^-O^  of  what  it 
would  be  if  the  globe  were  wholly  -iron.  In  weak  mag- 
netic fields  the  susceptibility  of  nickel  exceeds  by  about 
five  times  that  of  iron  ;  but  in  strong  fields  iron  is  more 
susceptible. 

The  coefficient  of  magnetic  induction,  or  per- 
meability, is  based  on  the  lines  of  magnetic  induction. 
The  number  of  magnetic  lines  that  run  through  unit 
area  of  cross  section,  at  any  point,  is  called  "the  mag- 
netic induction "  at  that  point :  it  is  denoted  by  the 
letter  B.  The  ratio  between  the  magnetic  induction 
and  the  magnetising  force  producing  it  is  expressed  by 
a  numerical  coefficient  of  induction,  or  permeability^  u. 
We  therefore  write 

B  =  fiH 
or  /*  =  f 9 

This  coefficient  is  always  positive  :  for  empty  space  it 
is  I,  for  air  it  is  practically  i  ;  for  magnetic  materials  it 
is  greater  than  I,  for  diamagnetic  materials  it  is  slightly 
less  than  i.  The  student  may  think  of  it  in  the  follow- 
ing way  :  Suppose  a  certain  magnetising  force  to  act  in 
a  certain  direction,  there  would  naturally  result  from  its 
action  induction  along  a  certain  number  of  lines  of  in- 


272 


ELEMENTARY  LESSONS  ON        [CHAP.  v. 


duction  (or  so-called  lines  of  force),  and  in  a  vacuum 
the  number  of  lines  would  numerically  represent  the 
magnetising  force.  But  if  the  space  considered  were 
occupied  by  iron  the  same  magnetising  force  would 
fnduce  many,  more  lines.  The  iron  has  a  sort  of  multi- 
plying power  or  specific  inductive  capacity,  or  conduc- 
tivity for  the  magnetic  lines.  This  permeability  is  easily 
calculated  from  the  susceptibility.  It  was  shown  at  end 
of  Art.  3 1 2  that  there  are  4?r  magnetic  lines  proceeding 
from  each  unit  of  pole  magnetism.  Hence  if,  as  shown 
above,  each  line  of  force  of  the  magnetising  field  pro- 
duces k'  units  of  magnetism  there  will  be  4,-nk  lines 
added  by  the  iron  to  each  I  line  in  the  field,  or  the 
multiplying  power  of  the  iron  /A  is  equal  to  i  +  4^. 
The  values  of  the  permeability,  like  those  of  suscepti- 
bility, decrease  as  the  magnetisation  of  the  iron  gets  in- 
creased towards  saturation.  In  the  following  Table  two 
sets  of  values  are  given  from  the  researches  of  Stole- 
tow,  and  the  more  recent  ones  of  Bidwell. 


H 

k 

I 

M 

B 

OBSERVATIONS  OF  STOLETOW. 

0-43 

0'44: 

3-20 
30-6 

21-5 

30-5 
174-0 

39-4 

9-24 
I3-45 
556-6 
1206- 

275-6 

3905 
2222 
504-2 

118-5 
171-8 

15427- 

OBSERVATIONS  OF  BIDWELL. 

3'9 
10-3 

40-  . 

151-0 
89-1 
30-7 

587 
918 
1226 

1899-1 
386-4 

7390 
15460- 

U5 

208- 

ti  -9 

7-0 

1370 

145* 

1507 

88-8 

17330 
18470 

.427- 

2-6 

1504 
1530 

45'3 
33'9 

19330 
19820 

CHAP,  v.]    ELECTRICITY  AND  MAGNETISM.  273 


According  to  Hopkinson  the  induction  B  for  cast 
iron  is  about  i  r,ooo,  in  a  field  H  of  220  :  the  residual 
induction  being  about  5000.  Bosanquet  finds  maxi- 
mum induction  B  for  charcoal  iron  and  wrought  iron 
from  16,800  to  about  19,000;  but  has  succeeded  in 
magnetising  a  wrought  iron  bar  so  that  the  induction  in 
the  middle  bit  of  the  bar  reached  2  9',  3  8  8.  Steel  con- 
taining 1  2  per  cent  of  manganese  is  curiously  non-mag- 
netic, Hopkinson  found  its  maximum  induction  only  310. 

314.  Potential  due  to  a  (Solenoidal)  Magnet. 
—  A  long  thin  uniformly  magnetised  magnet  exhibits 
free  magnetism  only  at  the  two  ends,  and  acts  on 
external  objects  just  as  if  there  were  two  equal  quantities 
of  opposite  kinds  of  magnetism  collected  at  these  two 
points.  Such  a  magnet  is  sometimes  called  a  solenoid 
to  distinguish  it  from  a  magnetic  shell  (Art.  107). 
Ordinary  straight  and  horse-shoe  shaped  magnets  are 
imperfect  solenoids.  The  magnetic  potential  due  to  a 
solenoid,  and  all  its  magnetic  effects,  depend  only  on 
the  position  of  its  two  poles,  and  on  their  strength,  and 
not  on  the  form  of  the  bar  betv/een  them,  whether  straight 
or  cun  p.d.  In  Art.  3  10  (<r)  was  given  the  rule  for  finding 
the  potential  due  to  a  system  of  poles.  Suppose  the 
two  poles  of  a  solenoid  have  strengths  +  m  and  —  in 
(taking  S.-se.eking  pole  as  of  negative  value),  and  that 
the  respective  distances  of  these  poles  from  an  external 
point  P,  are  r^  and  rt  :  then  the  potential  at  P  will  be, 

VF  =«(L_  -L). 

V  >-i  r*  / 

Suppose  a  magnet  curled  round  until  its  N.  and  S. 
poles  touch  one  another  :  it  will  not  act  as  a  magnet 
on  an  external  object,  and  will  have  no  "  field  "  (Art. 
105);  for  if  the  two  poles  are  in  contact,  their  distances 
r,  and  rt  to  an  external  point  P  will  be  equal,  and 

will  be  = 


-} 

r) 


315.    Potential    due    to   a   Magnetic    Shell.  — 
Gauss  demonstrated  that  the  potential  due  to  a  magnetic 


^4  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

shell  at  a  point  near  it  is  equal  to  the  strength  of  the 
shell  multiplied  by  the  solid-angle  subtended  by  the  shell 
at  that  point;  the  "  strength  "  of  a  magnetic  shell 
being  the  product  of  its  thickness  into  its  surface-density 
of  magnetisation. 

If  w'  represents  tne  solid-angle  subtended  at  the  point 
P,  and  i  the  strength  of  the  shell,  then 

VP    =   w  /. 

Proo£  —  To  establish  this  proposition  would  require  an  easy 
application  of  the  integral  calculus.  But  the  following  geo- 
metrical demonstration,  though  incomplete,  must  here  suffice. 

Let  us  consider  the  shell  as  comDosed,  like  that  drawn,  of 
&  series  of  small  elements  of 
thickness  /,  and  having  each  an 
area  of  surface  s.  The  whole 
solid  -angle  subtended  at  P  by 
the  shell  may  likewise  be  con- 
ceived as  made  up  of  a  number 
of  elementary  small  cones,  each 
of  solid  -angle  16  :  Let  r^  and  rz 
be  the  distances  from  P  to  the  F- 

two  faces  of  the  element  :  Let 

a  section  be  made  across  the  small  cone  ortnogonally,  or  at 
right  angles  to  rv  and  call  the  ,area  of  this  section  a  :  Let  the 
angle  between  the  surfaces  s  and  a  be  called  angle  ft  :  then 

s  =  -^-JT.  Let  *  be  the  "strength"  of  the  shell  '(i.e.  =  its 
surface-density  of  magnetisation  x  its  thickness)  ;  then  —  = 

surface-density  of  magnetisation,  and  s  '—   =  strength  of  either 

pole  of  the  little  magnet  =  m. 

-_          ,.  ,        .  area  of  us  orthogonal  section 

Now  solid  angle  t6  =  -  0-2  -  - 

N 


a  . 


therefore  a 

Hence      ** 


c/IXI.  v.]     ELECTRICITY  AND  MAGNETISM.  275 


But  the  potential  at  P  of  the  magnet  whose  pole  is  m,  will  1>2 


/  cos 


-   .L) 

ra  / 


but     -    -  SB     J  — ^  which  we  may  write  —  -  ..  •?• 

ri          ri  rirt  ^ 

because  rx  and  rs  may  be  made  as  nearly  equal  as  we  please. 

And  since  r±  —  r,    =   /  cos  /3 

/cos/3  \ 


f  cos  ft 
v  =    (W 


or  the  potential  due  to  the  element  of  the  shell  =  the.  strength 
of  the  shell  x  the  solid-angle  subtended  by  the  element'  of  the 
shell.  Hence,  if  V  be  the  sum  of  all  the  values  of  v-  for  all  the 
different  elements,  and  if  w  be  the  whole  solid-angle  (the  sum 
of  all  the  small  solid-angles  such  as  <£), 

Vp    =   U£ 

or,  the  potential  due  to  a  magnetic  shell  at  a  point  is  equal  to 
the  strength  of  the  shell  multiplied  by  the  solid-angle  subtended 
by  the  whole  of  the  shell  at  that  point. 

Hence  wt  represents  the  work  that  would  have  to  be 
done  on  or  by  a  unit-pole,  to  bring  it  up  from  an 
infinite  distance  to  the  point  P,  where  the  shell  subtends 
the  solid-angle  o>.  At  a  point  Q  where  the  solid-angle 
subtended  by  the  shell  is  different,  the  potential  will  be 
different,  the  difference  of  potential  between  P  and  Q 

being  ir         v  •  /  \ 

vd   -  Vp    =    *  (WQ   -  wp). 

If  a  magnet-pole  whose  strength  is  nt  were  brought 
up  to  P,  m  times  the  work  would  have  to  be  done,  or 
the  mutual  potential  would  be  =  MM. 

316.  Potential  of  a  Magnet-pole  on  a  Shell — 
It  is  evident  that  if  the  shell  of  strength  i  is  to  be 
placed  where  it  subtends  a  solid-angle  u  at  the  pole  nt, 
it  would  require  the  expenditure  of  the  same  amount  o/ 
work  to  bring  up  the  shell  from  an. infinite  distance 
on  the  one  hand,  as  to  bring  up  the  magnet-pole  :roiu 


276  ELEMENTARY  LESSONS  ON       [CHAI-.  v. 

an  infinite  distance  on  the  other ;  hence  mui  represents 
both  the  potential  of  the  pole  on  the  shell  and  the 
potential  of  the  shell  on  the  pole.  Now  the  lines  of 
force  from  a  pole  may  be  regarded  .as  proportional  in 
number  to  the  strength  of  the  pole,  and  from  a  single 
pole  they  would  radiate  out  in  all  directions  equally. 
Therefore,  if  a  magnet-pole  was  placed  at  P,  at  the  apex 
of  the  solid-angle  of  a  cone,  the  number  of  lines  of  force 
which  would  pass  through  the  solid-angle  would  be  pro- 
portional to  that  solid-angle.  It  is  therefore  convenient 
to  regard  tn<a  as  representing  the  number  of  lines  of  force 
of  the  pole  which  pass  through  the  shell,  and  we  may  call 
the  number  so  intercepted  N.  Hence  the  potential  of  a 
magnet-pole  on  a  magnetic  shell  is  equal  to  the  strength 
of  the  shell  multiplied  by  the  number  of  lines  of  force 
(due  to  the  magnet-pole)  which  pass  through  the  shell; 
or  V  =  N*.  If  either  the  shell  or  the  pole  were  moved 
to  a  point  where  a  different  number  of  lines  of  force 
were  cut,  then  the  difference  of  potential  would  be, 

VQ  -  VP  =  ±i  (NQ  -  NP). 

This  formula  is  of  great  importance  :  but  the  student 
must  be  specially  cautioned  as  to  the  signs  to  be 
attributed  in  applying  it  to  the  various  quantities.  A 
magnet  has  two  poles  (N.-seeking  and  S.-seeking),  whose 
strengths  are  -t-  m  and  —  m,  and  the  two  faces  of  a 
magnetic  shell  are  of  opposite  sign.  To  bring  up  a  N.- 
seeking  (or  +)  pole  against  the  repelling  force  of  the 
N.-seeking  face  of  a  magnetic  shell  requires  a  positive 
amount  of  work  to  be  done ;  and  their  mutual  reaction 
would  enable  work  to  be  done  afterwards  by  virtue  of 
their  position  :  in  this  case  then  the  potential  is  +.  But 
in  moving  a  N.-seeking  pole  up  to  the  S.-seeking  face  of 
a  shell  work  will  be  done  by  the  pole,  for  it  is  attracted 
up  ;  and  as  work  done  by  the  pole  may  be  regarded  as 
our  doing  negative  work,  the  potential  here  will  have  a 
negative  value. 


CITAP.  v.]      ELECTRICITY  AND  MAGNETISM.          277 

Again,  suppose  -we  could  bring  up  a  unit  N.-seeldng 
pole  against  the  repulsion  of  the  N.-seeking  face  of  a 
shell  of  strength  /,  and  should  push  it  right  up  to  the 
shell ;  when  it  actually  reached  the  plane  of  the  shell  the 
shell  would  occupy  a  whole  horizon,  or  half  the  whole 
space  around  the  pole,  the  solid-angle  it  subtended  being 
therefore  2-r,1  and  the  potential  will  be  +  2-r*.  If  we 
had  begun  at  the  S. -seeking  face,  the  potential  at  that 
face  would  be  -  2<n.  It  appears  then  that  the  potential 
alters  its  value  by  4-r/  on  passing  from  one  side  of  the 
shell  to  the  other. 

317.  Reaction  between  a  Pole  and  a  Magnetic 
ShelL — Again,  Figs.  52  and  53  will  show  graphically 
that  lines  of  force  from  two  poles  of  opposite  kind  run 
into  one  another,  whilst  those  from  similar  poles  turn 
aside  as  if  mutually  repellant.  If  a  N.-seeking  pole  be 
brought  up  to  the  N.-seeking  face  of  a  shell  few  or  none 
of  the  lines  of  force  of  the  magnet  will  cut  the'  shell ; 
whereas  if  a  N.-seeking  pole  be  brought  up  to  the 
S.-seeking  face  of  a  shell,  large  numbers  of  the  lines  will 
be  cut  by  the  shell  and  the  pole,  as  a  matter  of  fact,  will 
be  attracted  up  to  the  shell,  where  as  many  lines  of  force 
as  possible  are  cut  by  the  shell.  We  may  formulate  this 
action  by  saying  that  a  magnetic  shell  and  a  magnet-pole 
react  on  one  another  and  urge  one  another  in  such  a 
direction  as  to  make  the  number  of  lines  of  force  that  are 
cut  by  the  shell  a  maiimunl.  (Maxwell's  Rule,  Art.  193). 
Outside  the  attracting  face  of  the  shell  the  potential  is  —  «/, 
and  the  pole  moves  so  as  to  make  this  negative  quantity 
as  great  as  possible,  or  to  make  the  potential  a  minimum. 
Which  is  but  another  way  of  putting  the  matter  as  a 
particular  case  of  the  general  proposition  that  bodies 
tend  to  move  so  that  the  energy  they  possess  in  virtue 
of  their  position  tends  to  run  down  to  a  minimum. 

318.  Magnetic  Potential  due  to  Current. — The 
propositions  concerning  magnetic  shells  given  in  iVje 

I  Sec  note  on  Ways  of  Reckoning  Angles,  Art.  133. 


278  ELEMENTARY  LESSONS  ON        [CHAP.  v. 


preceding  paragraphs  derive  their  great  importance 
because  of  the  fact  laid  down  in  Art  192  that  circuits, 
traversed  by  currents  of  electricity,  behave  like  magnetic 
shells.  And  for  the  purpose  of  calculating  the  magnetic 
effects  due  to  currents  by  applying  these  theorems,  it  is 
necessary  to  adopt  the  electromagnetic  unit  of  the 
strength  of  current  explained  in  Art.  196.  If  we  adopt 
such  a  unit  we  may  at  once  go  back  to  Art.  3.1 5,  and 
take  the  theorems  about  magnetic  shells  as  being  also 
true  of  closed  voltaic  circuits. 

(a.)  Potential  due  to  closed  circuit  (compare 
Art.  315). 

The  potential  V  due  to  a  closed  voltaic  circuit  (traversed 
by  a  current)  at  a  point  P  near  it,  is  equal  to  the  strength 
of  the  current  multiplied  by  the  solid -angle  <a  sudtended 
by  the  circuit  at  that  point.  If  /  be  the  strength  of  the 
current  in  electromagnetic  units,  then 

VP  =    -  M. 

The  reason  for  adopting  the  negative  sign  is  the  following : — 
The  potential  (i.e.  the  work  done  on  a  unit  N. -seeking 
pole)  is  reckoned  positive  where  the  work  is  done 
against  repulsion  Now,  if  a  N.  -seeking  pole  is  to  be 
brought  up  to  a  point  opposite  the  repelling  face  of  a 
circuit,  it  must  (see  Fig.  115)  be  brought  up  to  that  face 
round  which  the  electricity  is  flowing  in  the  counter- 
clock-wise  or  negative  direction,  or  round  which  the 
current  must  be  considered  as  having  strength  =  —  i. 
The  student  may  be  helped  to  understand  this  conven- 
tion about  signs  by  remembering  (see  Fig.  115)  that 
when  he  is  looking  at  the  S.  -pole  of  an  electromagnet 
he  is  looking  along  the  magnetic  lines  of  force  in  their 
positive  direction,  and  that  the  current  is  running  clock- 
wise round  the  coil.  Or,  the  positive  direction  of  lines 
of  force  through  the  circuit  is  associated  with  a  (positive) 
rotation  round  the  circuit,  as  's  Jhe  forward  thrust  with 
the  right-handed  rotation  in  the  operation  of  driving  an 
ordinary  right-handed  screw. 

(£.)  At  a  point  Q,  where  the  solid -angle  subtended  by 


CHAP:  v.]     ELECTRICITY  AND  MAGNETISM.-         271 

the  circuit  is  &»Q  instead  of  wp,  the  potential  will  have  a 
different  value,  the  difference  of  potential,  being, 

VQ  -  VP  =   ~  *  («Q  -  WP). 

319.  (<r.)  Mutual  Potential  of  a  Magnet -pol 
and  a  Circuit. — If  a  magnet-pole  of  strength  m  wer 
brought  up  to  P,  where  the  circuit  subtends  a  solid-angle 
a,  from  an  infinite  distance  against  the  magnetic  forces 
exercised  by  the  current,  m  times  as  much  work  will  be 
done  as  if  the  magnet-pole  had  been  of  unit  strength,  and 
the  work  would  be  just  as  great  whether  the  pole  m  were 
brought  up  to  the  circuit,  or  the  circuit  up  to  the  pole. 
Hence,  the  mutual  potential  will  be 

-  mm. 

But,  as  in  Art.  316,  we  may  regard  mu  as  representing 
the  number  of  lines  of  force  of  the  pole  which  are 
intercepted  by  and  pass  through  the  circuit,  and  we 
may  write  N  for  that  number,  and  say 

V  =    -  *N, 

or  the  mutual  potential  of  a  magnet-pole  and  a  circuit 
is  equal  to  the  strength  of  the  current  multiplied  by  the 
number  bf  the  magnet-pole's  lines  of  force  that  are  inter- 
cepted by  the  circuit,  taken  with  reversed  sign. 

(</.)  As  in  the  case  of  the  magnetic  shell,  so  with  the 
circuit,  the  value  of  the  potential  changes  by  4-37  from  a 
point  on  one  side  of  the  circuit  to  a  point  just  on  the 
other  side ;  that  is  to  say,  being  —  2id  on  one  side  and 
+  2-r/  on  the  other  side,  work  equal  to  ^m  must  be 
done  in  carrying  a  unit-pole  from  one  side  to  the  other 
round  the  outside  of  the  circuit.  The  work  done  in 
thus  threading  the  circuit  along  a  path  looped  n  times 
round  it  would  be  4*1  vt. 

320.  (<?.)  Mutual  Potential  of  two  Circuits. — Two 
closed  circuits  will  have  a  mutual  potential,  depending  on 
the  strengths  of  their  respective  currents,  on  tfceir  distance 
apart,  and  on  their  form  and  position.      If  their  currents 


28o  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

be  respectively  /  and  **.  and  if  the  distance  between  t\vo 
elements  ds  and  ds'  of  the  circuits  be  called  r,  and  e  the 
angle  between  the  elements,  it  can  be  shown  that  their 

mutual  potential  is  =  -  iijj  ^-^  ds  ds'.    This  expressior 

represents  the  work  that  would  have  to  be  done  to 
bring  up  either  of  the  circuits  from  an  infinite  distance 
to  its  present  position  near  the  other,  and  is  a  negative 
quantity  if  they  attract  one  another.  Now,  suppose  the 
strength  of  current  in  each  circuit  to  be  unity  ;  their  mutual 

potential  will  in  that  case  ^f'^~  &  <&>  a  quantity  which 


depends  purely  upon  the  geometrical  form  and  position 
of  the  circuits,  and  for  which  \ve  may  substitute  the 
single  symbol  M,  which  we  will  call  the  "  coefficient  oj 
mutual  potential:"  we  may  now  write  the  mutual 
potential  of  the  two  circuits  when  the  currents  are  /  and 
f  as  =  -  «"M. 

But  we  have  seen  in  the  case  of  a  single  circuit  that 
we  may  represent  the  potential  between  a  circuit  and  a 
unit-pole  as  the  product  of  the  strength  of  the  current 
-  i  into  the  number  N  of  the  magnet-pole's  lines  of  force 
intercepted  by  the  circuit.  Hence  the  symbol  M  must 
represent  the  number  of  each  other's  lines  of  force 
mutually  intercepted  by  both  circuits,  if  each  carried 
unit  current.  If  we  call  the  two  circuits  A  and  B,  then. 
when  each  carries  unit  current,  A  intercepts  M  lines  of 
force  belonging  to  B,  and  B  intercepts  M  lines  of  force 
belonging  to  A. 

Now  suppose  both  currents  to  run  in  the  same 
(clock-wise)  direction  ;  the  front  or  S.-seeking  face  of  one 
circuit  will  be  opposite  to  the  back  or  N.-seeking  face  of 
the  other  circuit,  and  they  will  attract  one  another,  and 
will  actually  do  work  as  they  approach  one  another,  or 
(as  the  negative  sign  shows)  negative  work  will  be  dene 
in  bringing  up  one  to  the  other.  When  they  have 
attracted  one  another  up  as  much  as  possible  the  circuits 
will  coincide  in^  direction  and  position  as  nearly  as  can 


CHAP,  v.]      ELECTRICITY  AND  MAGNETISM.          281 

ever  be.  Their  potential  energy  will  have  run  down  to 
its  lowest  minimum,  their  mutual  potential  being  a  neg- 
ative maximum,  and  their  coefficient  of  mutual  potential 
M,  having  its  greatest  possible  value.  Two  circuits, 
then,  are  urged  so  that  their  coefficient  of  mutual  potential 
M  shall  have  the  greatest  possible  value.  This  justifies 
Maxwell's  Rule  (Art.  193),  because  M  represents  the 
number  of  lines  of  force  mutually  intercepted  by  both 
circuits.  And  since  in  this  position  each  circuit  induces 
as  many  lines  of  magnetic  force  as  possible  through  the 
other,  the  coefficient  of  mutual  potential  M  is  also  called 
the  coefficient  of  mutual  induction. 

NOTE  ON  MAGNETIC  AND  ELECTRO- 
MAGNETIC UNITS. 

821.  Magnetic  Units. — All  magnetic  quantities,  strength  of 
poles,  intensity  of  magnetisation,  etc.,  are  expressed  in  terms  of 
special  units  derived  from  the  fundamental  units  of  length,  mass, 
and  time,  explained  in  the  Note  on  Fundamental  and  Derivea 
Units  (Art.  254).  Most  of  the  following  units  have  been  directly 
explained  in  the  preceding  Lesson,  or  in  Lesson  XI.;  the  others 
follow  from  them. 

Unit  Strength  of  Magnetic  Pole. — The  unit  magnetic  pole  is 
one  of  such  a  strength,  that  when  placed  at  a  distance  of 
one  centimetre  (in  air)  from  a  similar  pole  of  equal 
strength,  repels  it  with  a  force  of  one  dyne  (Art.  125). 

Magnetic  Potential. — Magnetic  potential  being  measured  by 
work  done  in  moving  a  unit  magnetic  pole  -against  the 
•magnetic  forces,  the  unit  of  magnetic  potential  will  be 
measured  by  the  unit  of  work,  the  erg. 

Unit  Difference  of  Magnetic  Potential. — Unit  difference  of 
magnetic  potential  exists  between  two  points  when  it 
requires  the  expenditure  of  one  erg  of  work  to  bring  a 
(N.  -seeking)  unit  magnetic  pole  from  one  point  to  the 
other  against  the  magnetic  forces. 

Intensity  of  Magnetic  Field  is  measured  by  the  force  it  exerts 
upon  a  unit  magnetic  pole  :  hence, 

Unit  Intensity  of  Field  is  that  intensity  of  field  which  acts 
on  a  unit  (N.  -seeking)  pole  with  a  force  of  one  dyne. 


282  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

322.  Electromagnetic   Units. — The    preceding    magnetic 
units  give  rise  to  the  following  set  of  electrical  units,  in  which 
the  strength  of  currents,  etc.,  aie  expressed  in  magnetic  measure. 
The  relation  of  this   "  electromagnetic "   set   of  units   to   the 
''electrostatic"  set  of  units  of  Art.  257  is  explained  in  Art. 

365. 

Unit  Strength  of.  Current. — A  current  ha«  unit  strength  when 

one  centimetre  length  of  its  circuit  bent  into  an  arc  rf 
one  centimetre  radius  (so  as  to  be  always  one  centim. 
away  from  the  magnet-pole)  exerts  a  force  of  one  dyne 
on  a  unit  magnet-pole  placed  at  the  centre  (Art.  196). 

Unit  of  Quantity  of  Electricity  is  that  quantity  which  is 
conveyed  by  unit  current  in  one  second. 

Unit  of  Difference  of  Potential  (or  of  Electromotive-force). 
Potential  is  work  done  on  a  unit  of  electricity  ;  hence 
unit  difference  of  potential  exists  between  two  points 
when  it  requires  the  expenditure  of  one  erg  of  work  to 
bring  a  unit  of  +  electricity  from  one  point  to  the  other 
agaiiut  the  electric  force. 

Unit  of  Resistance. — A  conductor  posoesses  unit  resistance 
when  unit  difference  of  potential  between  its  ends  causes 
a  current  of  unit  strength  (i.e.  one  unit  of  quantity  per 
second)  to  flow  through  it. 

323.  Practical  Units — Several  of  the  above  <; absolute" 
units  would  be  inconveniently  large  and  others  inconveniently 
small  for  practical  use.     The  following  are  therefore  chosen 
instead,  as  electromagnetic  units  : — 

Electromotive-fora. — The  Volt,  =  io8  absolute  units  (being 
a  little  less  than  the  E.M.F.  of  one  Daniell's  cell). 

Resistance. — The  Ohm,  =  io9  absolute  units  of  resistance 
(and  theoretically  the  resistance  represented  by  the  velo- 
city of  one  earth-quadrant  per  second).  (See  Art.  364.) 

Current. — As  a  practical  unit  of  current,  that  furnished  by  a 
potential  of.  one  volt  though  one  ohm  is  taken,  being 
io— 1  of  an  absolute  (electro-magnetic)  unit  of  current, 
and  is  known  as  one  Ampere  (formerly  one  "weber"). 

Quantity. — The  Coulomb,  =  io-1  absolute  units  of  quantity 

of  the  electromagnetic  system. 
Capacity. — The   Farad,  =  io-9   (or   one   one- thousand  - 

millionth)  of  absolute  unit  of  capacity. 


CHAP,  v.]      ELECTRICITY  AND  MAGNETISM. 


283 


Seeing,  however,  that  quantities  a  million  times  as  great  as 
some  of  these,  and  a  million  times  as  small  as  some,  have  to  be 
measured  by  electricians,  the  prefixes  mega-  and  micro-  are 
sometimes  used  to  signify  respectively  "  one  million  "  and  "  one- 
millionth  part."  Thus  a  megohm  is  a  resistance  of  one  million 
ohms,  a  microfarad  a  capacity  of  i.00o.0oo  °^  a  fara<*»  etc* 
The  prefix  milli-  is  frequently  used  for  "one-thousandth  part ;" 
thus  a  milli-amptre  is  the  thousandth  part  of  one  ampere. 

This  system  of  "practical"  units  was  devised  by  a  committee 
of  the  British  Association,  who  also  determined  the  value  of  the 
"ohm"  by  experiment,  and  constructed  standard  resistance 
coils  of  german-silver,  called  "B.  A.  Units"  or  "ohms." 
The  "  practical "  system  may  be  regarded  as  a  system  of  units 
derived  not  from  the  fundamental  units  of  centimetre,  gramme, 
and  second,  but  from  a  system  in  which,  while  the  unit  of  time 
remains  the  second,  the  units  of  length  and  mass  are  respectively 
the  earth-quadrant  and  10  — n  gramme. 

324  Dimensions  of  Magnetic  and  Electromagnetic  Units. 
— The  fundamental  idea  of  "dimensions"  is  explained  in  Art. 
258.  A  little  consideration  will  enable  the  student  to  deduce 
for  himself  the  following  table — 


UNITS. 


(Magnetic. ) 

Strength  of  pole 
Quantity  of  magnetism 

Magnetic  Potential 
Intensity  of  Field 

v  Electro-magnetic. ) 
Current  (strength) 
Quantity 

Potential  ) 

Electromotive- Force  \ 

Resistance 
Capacity 


Vforce  X  (distance)* 

work  -T-  strength  of  pole 
force  -f-  strength  of  pole 

intensity  of  field  x  length 
current  x  time 

work  -f-  quantity 

E.M.F.  -7-  current 
quantity  -5-  potential 


DIMENSIONS. 


ELEMENTARY  LESSONS  OX        [CHAP.  v. 


NOTE  ON  MEASUREMENT  OF  EARTH'S  MAGNETIC 
FORCE  IN  ABSOLUTE  UNITS. 

325a.  The  intensity  of  the  earth's  magnetic  force  at  any  place  is 
the  force  with  which  a  magnet-pole  of  unit  strength  is  attracted. 
As  explained  in  Art.  138,  it  is  usual  to  measure  the  horizontal 
component  H  of  this  force,  and  from  this  and  the  cosine  of  the 
angle  of  dip  to  calculate  the  total  force  I.  as  the  direct  deter- 
mination of  the  total  force  is  surrounded  with  difficulties.  To 
determine  H  in  absolute  (or  C.G.S.)  units,  it  is  necessary  to 
make  two  observations  with  a  magnet  of  magnetic  moment  M  ; 
(the  magnetic  moment  being,  as  mentioned  in  Art..  313,  the 
product  of  its  length  into  the  strength  of  one  of  its  poles).  In 
one  of  these  observations  the  product  MH  is  detennined  by  a 

method  of  oscillations ;  hi  the  second  the  quotient  77  is  deter- 
mined by  a  particular  method  of  deflection.  The  square  root  of 
the  quantity  obtained  by  dividing  the  former  by  the  latter  will, 
of  course,  give  H. 

(i.)  Determination  o/MH. — The  time  /  of  a  complete  oscilla- 
tion to-and-fro  of  a  magnetic  bar  is 


/  =  27r  V  feT1 

where  K  is  the  "  moment  of  inertia  "  of  the  magnet.  This 
formula  is,  however,  only  true  for  very  small  arcs  of  vibration. 
By  simple  algebra  it  follows  that 

HM  = 


Of  these  quantities  /  is  ascertained  by  a  direct  observation  01 
the  time  of  oscillation  of  the  magnet  hung  by  a  torsionless  fabre  : 
and  K  can  be  either  determined  experimentally  or  by  one  of  the 
following  formulae : — 

f  P        a"  \ 
For  a  round  bar  K  «=«/( h   — ), 

(/a   +  ^2  \ 
I  > 

where  w  is  the   mass  of  the  bar  in  grammes,  /  its  length,  a 


CHAP,  v.]     ELECTRICITY.  AND  MAGNETISM.  285 


its  radius  (if  round),  *  its  breadth,  measured  horizontally  (if 

rectangular). 

M 
(ii.)  Determination  of  -g.  —  The  magnet  is  next  caused  to 

deflect  a  small  magnetic  needle  in  the  following  manner, 
"broadside  on."  The  magnet  is  laid  horizontally  at  right 
angles  to  the  magnetic  meridian,  and  so  that  its  middle  point  is 
(magnetically)  due  south  or  due  north  of  the  small  needle,  and 
at  a  distance  r  from  its  centre.  Lying  thus  broadside  to  the 
small  needle  its  N.-pole  will  repel,  and  its  S.-pole  attract,  the 
N.-pole  of  the  needle,  and  will  exercise  contrary  actions  on  the 
S.-pole  of  the  needle.  The  total  action  of  the  magnet  upon  the 
needle  will  be  to  deflect  the  latter  through  an  angle  8,  whose 

M 
tangent  is  directly  proportional  to  -jj,   and   inversely  propor- 

tional to  the  cube  of  the  distance  r  ;  or 

M         ,  . 

-g  =  r3  tan  o. 

Dividing  the  former  equation  by  this,  and  taking  the  square  root, 
we  get, 


"  / 

"7V  ' 


TT  *•"  /  «• 


tan  «. 


NOTE  ON  INDEX  NOTATION. 

325b.  Seeing  that  electricians  have  to  deal  with  quantities 
requiring  in  some  cases  very  large  numbers,  and  in  other  cases 
very  small  numbers,  to  express  them,  a  system  of  index  notation 
is  adopted,  in  order  to  obviate  the  use  of  long  rows  of  cyphers. 
In  this  system  the  significant  figures  only  of  a  quantity  are  put 
down,  the  cyphers  at  the  end,  or  (in  the  case  of  a  long  decimal) 
at  the  beginning,  being  indicated  by  an  index  written  above. 
Accordingly,  we  may  write  a  thousand  (=iox  lox  10)  as 
io8,  and  the  quantity  42,000  may  be  written  42  x  io3.  The 
British  National  Debt  of  ^"770,000,000  may  be  written  .£77  x 
ior.  Fractional  quantities  will  have  negative  indices  when 
written  as  exponents.  Thus  ^  (=  o-oi),  =  I  -J-  io  -5- 
10  =  io-2.  And  so  the  decimal  0-00028  will  be  written 
28  x  io~5  (being  =  28  x  -ooooi).  The  convenience  of  this 
method  will  be  seen  by  an  example  or  two  on  electricity. 
The  electrostatic  capacity  of  the  earth  is  630,000,000  times 


286 


ELEMENTARY  LESSONS  ON        [CHAP.  v. 


that  of  a  sphere  of  one  centimetre  radius,  =  63  x  io7  (electro- 
static) units  The  -magnetic  moment  of  the  earth  is,  accenting 
to  Gauss,  no  less  than  85,000,000,000,000,000,000,000,000 
times  that  .of  a  magnet  of  unit  strength  and  centim.  length,  i.e. 
its  magnetic  moment  is  85  x  io24  units.  The  resistance  of 
selenium  is  about  40,000,000,000,  or  4  x  io10  times  as  great  as 
that  of  copper ;  that  of  air  is  about  io26,  or 

i  oo,  ooo,  ooo,  ooo,  ooo,  ooo,  ooo,  ooo,  ooo 

times  as  great.  The  velocity  of  light  is  about  30,000,000,000 
centimetics  per  second,  or  3  x  io10.  As  a  final  example  we 
may  state  that  the  number  of  atoms  in  the  universe,  as  far  as 
the  nearest  fixed  star,  can  be  shown  to  be  certainly  fewer  than 
7  x  io91 

LESSON  XXVI. — Electromagnets. 

32S.  Electromagnets. — In  1820,  almost  immedi- 
ately after  Oerstedt's  discovery  of  the  action  of  the 
electiic  current  on  a  magnet  needle,  Arago  and  Davy 
independently  discovered  how  to  magnetise  iron  and 
steel  by  causing  currents  of  electricity  to  circulate  round 
them  in  spiral  coils  of  wire.  The  method  is  shown  in  the 


Fig.  114. 


simple  diagram  of  Fig.  114,  where  a  current  from  a 
single  cell  is  jjassed  through  a  spiral  coil  of  wire,  in  the 


CHAP,  v.]      ELECTRICITY  AND  MAGNETISM.         287 

hello w  of  which  is  placed  a  bar  of  iron  or  steel;  which  is 
thereby  magnetised.  The  separate  turns  of  the  coil 
must  not  touch  one  another  or  the  central  bar,  other- 
wise the  current  will  take  the  shortest  road  open  to  it 
and  will  not  traverse  the  whole  of  the  coils.  .To  pre- 
vent such  short-circuiting  by  contact  the  wire  of  the  coil 
should  be  overspun  with  silk  or  cotton  (in  the  latter  case 
insulation  is  improved  by  steeping  the  cotton  covering  in 
melted  paraffin  wax)  or  covered  with  a  layer  of  gutta- 
percha.  If  the  bar  be  of  iron  it  will  be  a  magnet  only 
so  long  as  the  current  flows  ;  and  an  iron  bar  thus  sur- 
rounded with  a  coil  of  wire  for  the  purpose  of  magnetising 
it  by  an  electric  current  is  called  an  Electromagnet. 
Sturgeon,  who  gave  this  name,  applied  the  discoveries 
of  Davy  and  Arago  to  the  construction  of  electromagnets 
far  more  powerful  than  any  magnets  previously  made. 
It  was  first  shown  by  Henry  that  when  electromagnets 
are  required  to  work  at  distant  end  of  a  long  line  they 
must  be  wound  with  many  turns  of  fine  wire. 

By  applying  Ampere's  Rule  (Art.  186),  we  can  find 
which  end  of  an  electromagnet  will  be  the  N. -seeking 
pole ;  for,  imagining  ourselves  to  be  swimming  in  the 
current  (Fig.  114),  and  to  face  towards  the  centre  where 
the  iron  bar  is,  the  N. -seeking  pole  will  be  on  the  left. 
It  is  convenient  to  remember  this  relation  by  the  fol- 
lowing rules : — Looking  at  the  S.-seeking  pole  of  an. 
electromagnet.  Hie  magnetising  currents  are  circulating 
round  it  in  the  same  cyclic  direction  as  the  hands  of  a 
clock  move;  and,  looking  at 
the  N. -seeking  pole  of  an 
electromagnet^  the  magnetis- 
ing currents  are  circulating 
round  it  in  the  opposite  cyclic 
direction  to  that  of  the  hands 
of  a  clock.  Fig.  115  shows  this  graphically.  These 
rules  are  true,  no  matter  whether  the  beginning  of  the 
coils .  is  at  the  end  near  the  observer,  or  at  the  farther 


288 


ELEMENTARY  LESSONS  ON        [CHAP.  v. 


end  from  him,  i.e.  whether  the  spiral  be  a  right-handed 
screw,  or  (as  in  Fig.  114)  a  left-handed  screw.  It  will 
be  just  the  same  thing,  so  far  as  the  magnetising  power 
is  concerned,  if  the  coils  begin  at  one  end  and  run  to 
the  other  and  back  to  where  they  began  ;  or  they  may 
begin  half-way  along  the  bar  and  run  to  one  end  and 
then  back  to  the  other  :  the  one  important  thing  to  know 
is  which  way  the  current  flows  round  the  bar  when  you 
look  at  it  end-on. 

327.  Construction  of  Electromagnets.  —  The 
most  useful  form  of  electromagnet  is  that  in  which  the 

iron  core  is  bent,  into  the 
form  of  a  horse-shoe,  so  that 
both  poles  may  be  applied 
to  one  iron  armature.  In 
this  case  it  is  usual  to  divide 
the  coils  into  two  parts  wound 
on  bobbins,  as  in  Figs.  116 
and  1 1 7.  The  electromagnet 
depicted  in  Fig.  117  is  of  a 
form  adapted  for  laboratory 
experiments,  and  has  mov- 
able coils  which  are  slipped 
A  special  form  of  electromagnet 
devised  by  Ruhmkorff  for  experiments  on  diamagnetism 
is  shown  in  Fig.  127.  The  great  usefulness  of  the 
electromagnet  in  its  application  to  electric  bells  and 
telegraphic  instruments  lies  in  the  fact  that  Us  magnet- 
ism is  under  the  control  of  the  current;  when  circuit  is 
"  made  "  it  becomes  a  magnet,  when  circuit  is  "broken  " 
it  ceases  to  act  as  a  magnet. 

Many  special  forms  of  electromagnet  have  been  de- 
vised for  special  purposes.  To  give  a  very  powerful 
attraction  at  very  short  distances,  a  short  cylindrical 
electromagnet  surrounded  by  an  outer  iron  tube,  united 
at  the  bottom  by  iron  to  the  iron  core,  is  found  best 
To  give  a  gentle  pull  over  a  long  range  a  solenoid  (Art. 


Fig.  116. 

on  over  the  iron  cores. 


CHAP,  v.]    ELECTRICITY  AND  MAGNETISM. 


289 


329),  having  a  long  movable  iron  core  is  used  For 
giving  a  very  quick -acting  magnet  the  coils  should  not 
be  wound  all  along  the  iron,  but  only  round  the  poles. 
As  a  rule  the  iron  parts,  including  the  yoke  and  arma- 


Fig.  117. 

ture,  should  form  as  nearly  as  possible  a  closed  magnetic 
circuit.  The  cross-sections  of  yokes  should  be  thicker 
than  those  of  the  cores. 

328.  Lifting-power  of  Electromagnets. — The 
lifting-power  of  an  electromagnet  depends  not  only  on  its 
"  magnetic  strength,"  but  also  upon  its  form,  and  on  the 
shape  of  its  poles,  and  on  the  form  of  the  soft  iron 
armature  which  it  attracts.  It  should  be  so  arranged 
that  as  many  lines  of  force  as  possible  should  run  through 
the  armature,  and  the  armature  itself  should  contain  a 


290  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

sufficient  mass  of  iron.  Joule  designed  a  powerful  electro- 
magnet, capable  of  supporting  over  a  ton.  The  maximum 
attraction  he  could  produce  between  an  electromagnet 
and  its  armature  was  200  Ibs.  per  square  inch,  or  about 
13,800.000  dynes  per  square  centimetre.  Bidwell  has 
found  the  attraction  to  go  up  to  226-3  Ibs.  per  square 
inch  when  the  wrought  iron  core  was  saturated  up  to 
19,820  magnetic  lines  to  the  square  centimetre.  It  can 
be  shown  that,  when  the  iron  is  far  from  saturation,  the 
attraction  of  an  armature  of  soft  iron  is  proportional 
to  the  square  of  the  "  magnetic  strength  "  of  the  clectro- 
magnetj  for,  suppose  an  electromagnet  to  have  its  strength 
doubled,  it  will  induce  the  opposite  kind  of  magnetisa- 
tion twice  as  strongly  as  before  in  the  iron  armature, 
and  the  resulting  force  (which  is  proportional  to  the 
product  of  the  two  strengths)  will  be  four  times  as  great 
as  at  first. 

329.  Solenoid. — Without  any  central  bar  of  iron  or 
steel  a  spiral  coil  of  wire  traversed  by  a  current  acts  as 
an  electromagnet  (though  not  so  powerfully  as  when  an 
iron  core  is  placed  in  it).  Such  a  coil  is  sometimes 
termed  a  solenoid.  A  solenoid  has  two  poles  and  a 

neutral  equatorial 
region.  Ampere 
found  that  it  v/ill 
attract  magnets  and 
be  attracted  by  mag- 
nets. It  will  attract 
another  solenoid;  it 
has  a  magnetic  field 


^ U  (JUUJ 

Fig.  x  resembling       gene- 

rally that  of  a  bar 
magnet.  If  so  arranged  that  it  can  turn  round  a  vertical 
axis,  it  will  set  itself  in  a  North  and  South  direction 
along  the  magnetic  meridian.  Fig.  I J  8  shows  a  solenoid 
arranged  with  pivots,  by  which  it  can  be  suspended  to  a 
"table,"  like  that  shown  in  Fig.  121, 


CHAP,  v.]    ELECTRICITY  AND  MAGNETISM.  291 


Reference  to  Fig.  86  and  to  Art.  192  will  recall  how 
a  single  loop  of  a  circuit  acts  as  a  magnetic  shell  of 
equivalent  form  and  strength.  A  solenoid  may  be  re- 
garded as  made  up  of  a  series  of  such  magnetic  shells 
placed  upon  one  another,  all  their  N.-seeking  faces  being 
turned  the  same  way.  Since  the  same  quantity  of 
electricity  flows  round  each  loop  of  the  spiral  coil  the 
loops  will  be  of  equal  magnetic  strength,  and  the  total 
magnetic  strength  of  the  solenoid  will  be  just  in  propor- 
tion ,td  the  number  of  turns  in  the  coil ;  and  if  there  be 
n  turns,  the  number  of  magnetic  lines  of  force  running 
through  the  .solenoid  will  •  be  n  times  as  great  as  the 
•numbes*  due  to  one  single  turn.  The  use  of  'the  iron 
core  is  by  its  greater  magnetic  induction  to  concentrate 
and  increase  the  available  number  of  lines  of  force  at 
definite  poles.  The  student  has  been  told  (Art  191) 
that  the  lines  of  force  due  to  a  current  flowing  in  a  wire 
are  closed  curves,  approximately  circles  (see  Fig!  85), 
round  the  wire.  If  there  were  no  iron  core  many  of 
these  little  circular  lines  of  force  would  simply  remain  as 
small  closed  curves  around  their  own  wire  -j  •  but,  since 
iron  has  a  high  coefficient  of  magnetic  induction,  where 
the  wire  passes  near  an  iron  core  the  lines  of  force  alter 
their  shape,  and  instead  of  being  little  circles  around  the 
separate  wires,  run  through  the  iron  core  from  end  to 
end,  and  round  outside  from  one  pole  back  to  the 
other,  as  in  a  steel  magnet.  A  few  of  the  lines  of  force 
do  this  when  there  is  no  iron  ;  almost  all  of  them,  do  this 
when  there  is  iron.  Hence  the  electromagnet  'with  its 
iron  core  has  enormously  stronger  poles  than  the  spiral 
coils  of  the  circuit  would  have  alone. 

In  a  long  straight  solenoid  without  an  iron  core  it  is 
easy  to  calculate  approximately  the  intensity  of  the  mag- 
netic field  produced  by  the  current.  For,  as  we  have 
seen  in  Art.  3 1 9,  the  work  done  on  a  unit  magnetic  pole 
in  moving  it  (against  the  magnetic  forces)  along  a.  path 
which  threads  through  the  circuit  #_times  is/equal  to 


292  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

fergs,  where  the  current  *  is  expressed  in  absolute  units 
(Art.  196).  But  since  the  work  done  on  a  unit  pole 
measures  the  magnetic  potential  (Art.  310),  we  may  say 
that  the  difference  of  magnetic  potential  between  one 
end  and  the  other  of  the  long  solenoid  is  equal  to  4irm. 
But  when  the  magnetic  potential  changes  as  you  go 
along  a  line,  the  rate  of  change  of  potential  per  unit  of 
length  is  a  measure  of  the  magnetic  force  (Art.  310,  e), 
If  /  be  the  length  of  the  solenoid  in  centimetres  then 
tprni  -f-  /  will  be  the  intensity  of  the  magnetic  force  in- 
r!de  the  solenoid.  And  since  the  intensity  of  the  mag- 
netic force  is  the  same  thing  as  the  intensity  of  the 
magnetic  field  at  that  point,  we  may  say  that  this  num- 
ber represents  the  number  of  lines  of  magnetic  force  per 
square  centimetre  of  the  cross-section  of  the  solenoid. 
If  H  stands  for  the  intensity  of  the  field  thus  produced 
inside  the  solenoid,  and  if  the  radius  of  the  spirals  be  r, 
and  the  whole  number  of  magnetic  lines  N  running 
through  the  solenoid  from  end  to  end  will  be  equal 
H  x  Trr2.  Hence  we  have  — 


H  (inside  solenoid)  = 
N  (through  solenoid)  =  w2  x 

and  since  (see  Art.  312)  4?r  magnetic  lines  go  to  one 
unit  of  magnetism,  the  solenoid  will  act  as  if  it  had  at 
its  ends  as  the  amount  of  magnetism  m  in  its  poles  — 


If  the  current  is  expressed  in  amperes  —  for  which 
we  may  use  the  letter  C  —  we  must  remember  that  ten 
amperes  equal  one  absolute  unit  (Art.  196),  and  there- 
fore C  -5-  10  =  /.  The  formulas  will  then  become  — 

H  =  *L  C« 


.  v.]    ELECTRICITY  AND  MAGNETISM. 


293 


N 


in 


137 


Cn. 


It  will  be  noticed  that  for  any  solenoid  of  given  length 
and  radius  the  three  magnetic  quantities  H  (interior 
magnetic  force),  N  (total  magnetic  lines),  and  m  (strength 
of  poles)  are  proportional  to  the  amperes  of  current  and 
to  the  number  of  turns  in  the  coil.  The  product  Cn 
which  thus  comes  into  all  solenoid  formulas  is  ofteri 
referred  to  as  the  number  of  ampere-turns. 

33O.  The  Laws  of  the  Electromagnet. — The 
exact  laws  governing  the  electromagnet  are  somewhat 
complicated ;  but  it  is  easy  to  give  certain  rules  which 
are  approximately  true.  The  current  circulating  in  the 
coils  exercises  a  magnetising  force,  and  this  magnetising 
force  produces  in  the  iron  core  a  certain  amount  of 
magnetism.  But  the  amount  of  magnetism  produced 
in  the  core  depends  on  many  other  things  beside  the 
intensity  of  the  magnetising  force  ;  for  instance,  it  de- 
pends on  the 
quality  of  the 
iron,  on  its  sec- 
tional area,  and 
on  its  length 
and  form.  The 
data  respecting 
magnetic  per- 
meability and 
saturation  of 
iron  in  Art.  313 
are  all-import- 
ant. Every 
electromagnet 
shows  the  same  general  set  of  facts — that  with  small 
exciting  currents  there  is  little  magnetism  produced,  with 
.larger  exciting  power  there  is  more  magnetism,  and  that 


m 


Q 

Fig.  n8  (bis). 


294  ELEMENTARY  LESSONS  ON        [CHAP.  V. 

with  very  great  exciting  power  the  iron  becomes  practi- 
cally saturated  and  will  take  up  very  little  additional 
magnetism.  The  curve  given  in  Fig.  1 1 8  (bis}  is  char- 
acteristic of  the  relation  between  exciting  power  and  the 
resulting  magnetism.  The  numbers  of  amperes  of  cur- 
rent C  (or,  if  preferred,  the  number  of  ampere-turns  Cn) 
are  plotted  out  horizontally  to  scale,  and  the  correspond- 
ing amount  of  magnetism  m  vertically.  For  example, 
when  the  exciting  current  has  the  value  indicated  to  scale 
by  the  length  of  the  line  OO,  the  amount  of  magnetism 
was  found  to  be  such,  on  its  scale,  as  to  be  represented 
by  the  length  QP.  The  point  P  is  a  point  on  the  curve. 
It  begins  at  O,  no  magnetism  when  there  is  no  current ; 
then  it  rises  steeply  and  obliquely  for  some  time,  then 
bends  over  and  at  S  becomes  nearly  horizontal,  the  iron 
being  nearly  saturated.  The  dotted  curve  corresponds 
to,the  values  of  magnetism  found  when  the  exciting 
jcurrent  is  gradually  decreased.  It  will  be  noted  that 
when  the  current  is  reduced  to  zero  there  is  still  some 
magnetism  left.  Many  attempts  have  been  made 
to  represent  by  algebraic  formulae  the  facts  that  are 
thus  graphically  exhibited.  Some  of  these  deserve 
mention. 

Formula  of  Lenz  and •  Jacobi. — According  to  Lenz 
and  Jacobi  the  magnetism  of  an  electromagnet  is  pro- 
portional to  the  current  and  to  the  nit  vibe  r  of  turns  of 
wire  in  the  coil — in  other  words,  is  proportional  to  the 
ampere-turns.  Or, in  symbols — 

m  =  anC, 

where  a  is  a  constant  depending  on  the  quantity,  quality, 
and  form  of  iron.  This  rule  is,  however,  only  true 
when  the  iron  core  is  still  far  from  being  "  saturated." 
If  the  iron  is  already  strongly  magnetised — as  at  P  in 
the  Fig. — a  current  twice  as  strong  will  not  double  the 
magnetisation  in  the  iron.  Joule  in  1847  showed  this 
tendency  to  depart  from  a  simply  proportion. 


CHAP,  v.]    ELECTRICITY  AND  MAGNETISM.  295 

Formula  of  Miiller.  —  Miiller  gave  the  following 
approximate  rule:  —  The  strength  of  an  electromagnet 
is  proportional  to  the  angle  whose  tangent  is  the  strength 
of  the  magnetising  current;  or 

m  =  A  tan-1  C, 

where  C  is  the  magnetising  current,  and  A  a  constant 
depending  on  the  construction  of  the  particular  magnet. 
If  the  student  will  look  at  Fig.  90  and  imagine  the 
diyisions  of  the  horizontal  tangent  line  OT  to  represent 
strengths  of  current,  and  the  number  of  degrees  of  arc 
intercepted  by  the  oblique  lines  to  represent  strengths 
of  magnetism,  he  will  see  that  even  if  OT  be  made  in- 
finitely long,  the  intercepted  angle  can  never  exceed  90°. 
Formula  of  Lamont  and  Frolich.  —  A  simpler  ex- 
pression, and  one  more  easy  for  algebraic  calculation 
has  lately  come  into  use,  and  forms  the  basis  of  Frolich's 
calculations  about  dynamo-electric  machines.  We  may 
write  it  thus  :  — 

w-=-Mrr^c  >' 

where  M  and  b  are  constants  depending  on  the  form, 
quality,  and  quantity  of  the  iron,  and  on  the  winding  of 
the  coil.  The  constant  b  is  the  reciprocal  of  that  number 
of  amperes  which  would  make  m  equal  to  half  possible 
maximum  of  magnetism.  Another  form  of  this  equation 
is  — 


T> 

m  =  B 


I  +  <r«C 


therein  B  is  a  constant  depending  on  the  construction 
and  the  quality  of  the  iron,  and  <r  another  constant  (a 
small  fraction)  depending  on  the  quality  and  quantity  of 
the  iron,  and  equal  to  the  reciprocal  of  that  number  of 
ampere-turns  which  would  bring  the  magnetism  uo  to 
half-saturation. 

Yet  another  form  of  this  equation  is  of  use  to  express 


296  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

the  number  of  magnetic  lines  N  proceeding  from  the 
pole  of  the  electromagnet  — 


N 


where  Y  represents  the  maximum  number  of  magnetic 
lines  that  there  would  be  if  the  magnetising  current 
were  indefinitely  increased  and  the  iron  core  saturated, 
and  C  stands  for  that  number  of  amperes  which  would 
bring  the  magnetism  up  to  half-saturation. 

Hopkinsoris  Formula.  —  Hopkinson  has  shown  that  it 
is  possible  to  calculate  N  by  a  process  resembling  the 
calculations  made  according  to  Ohm's  law  for  electric 
circuits.  We  may  look  upon  the  iron  cores  and  the 
armature  of  an  electromagnet  as  constituting,  together 
with  the  spaces  between,  a  sort  of  magnetic  circuit 
traversed  by  the  magnetic  lines.  Just  as  we  can  cal- 
culate in  an  electric  circuit  the  amount  of  current  when 
we  know  the  electromotive-force  and  the  electric  resist- 
ance round  the  circuit,  so  in  a  magnetic  circuit  we  can 
calculate  N  if  we  know  the  magnetomotive-force  (or 
the  line-integral  of  the  magnetising  forces  acting  round 
the  circuit)  and  the  several  resistances  of  the  different 
parts  of  the  circuit.  Now  the  magnetomotive  -force  is 


equal  to  (see  Arts.  319,  d,  and  329)  ^irCn  •-  10.  The 
magnetic  resistance  of  any  magnetic  conductor  is  pro- 
portional to  its  length,  and  inversely  proportional  to  its 
sectional  area  and  to  its  permeability.  Suppose  then 
we  have  a  magnetic  circuit  made  up  of  three  parts  —  a 
curved  iron  core  of  length  /1}  section  sv  and  permeability 
/xx  ;  an  armature  of  length  /2,  section  sz,  and  permeability 
/u-2  ;  two  air-gaps  between  them,  of  length  (from  iron  to 
iron)  of  /3,  section  (equal  to  area  of  polar  surface)  J3, 
and  of  unit  permeability  (for  air,  p  —  i)  ;  then  the  re- 
sistances of  these  three  parts  will  be  respectively 


CHAP,  v.]    ELECTRICITY  AND  MAGNETISM.  297 

Then   dividing   the   magnetomotive-force   by  the   total 
magnetic  resistance  we  get — 


N 


giving  the  number  of  magnetic  lines  of  the  magnet  in 
terms  of  the  ampere-turns  of  excitation.  It  is  necessary, 
however,  to  know  the  values  of  p  of  the  various  pieces 
of  iron  at  the  various  stages  of  excitation.  Hopkinscn 
has  applied  this  formula  with  great  success  in  calcula- 
tions about  dynamo-electric  machines.  Analogous  for- 
mulas have  been  used  by  Rowland  and  by  Kapp. 

It  may  be  noted  that  when  electromagnets  are  wound 
with  many  turns  of  fine  wire,  these  coils  will  add  to  the 
electric  resistance  of  the  circuit,  and  will  tend  to  diminish 
the  current  This  has  an  important  bearing  on  the 
construction  of  telegraphic  and  other  instruments  ;  for 
while  electromagnets  with  "long  coils,"  consisting  of 
many  turns  of  fine  wire,  must  be  used  on  long  circuits 
where  there  is  great  resistance,  such  an  instrument 
would  be  of  no  service  in  a  circuit  of  very  small  resist- 
ance, for  the  resistance  of  a  long  thin  coil  would  be 
disproportionately  great  :"  here  a  short  coil  of  few  turns 
of  stout  wire  would  be  appropriate.  (See  Art.  352.) 

As  the  magnetism,  of  the  magnet  depends  on  the 
number  of  ampere-turns,  it  should  make  no  matter 
whether  the  coils  are  bigger  than  the  core  or  whether 
they  enwrap  it  quite  closely.  If  there  were  no  magnetic 
leakage  this  would  be  true  in  one  sense  :  but  it  wastes 
more  battery  power  to  drive  the  current  round  coils  of 
larger  diameter,  because  of  the  greater  resistance  of  the 
greater  length  of  wire.  Hence  in  well  -constructed 
electromagnets  tf-e  coils  are  all  wound  as  closely  to  the 
iron  core  as  is  consistent  with'  good  insulation.  Also 
the  iron  is  chosen  as  thick  as  possible,  as  permeable  as 


298  ELEMFNTARY  LESSONS  ON        [CHAP.  v. 

possible,  and  forming  as  compact  a  magnetic  circuit  as 
possible,  so  that  the  magnetic  resistance  may  be  reduced 
to  its  utmost,  giving  the  greatest  amount  of  magnetism 
-for  the  number  of  ampere-turns  of  excitation.  This  is 
why  horse-shoe-shaped  electi  omagnets  are  more  powerful 
than  straight  electromagnets  of  equal  weight. 

It  requires  time  to  magnetise  an  iron  core.  This  is 
partly  due  to  the  fact  that  a  current,  when  the  circuit  is 
first  made,  does  not  instantly  attain  its  full  strength, 
being  retarded  by  the  self-induced  counter-electromotive- 
force  (Art.  404) ;  it  is  partly  due  to  the  presence  of 
transient  reverse  induction  currents  (Art.  393)  in  the 
iron  itself.  Faraday's  large  electromagnet  at  the  Royal 
Institution  takes  about  two  seconds  to  attain  its  maxi- 
mum stiength.  The  electromagnets  of  large  dynamo 
machines  often  take  ten  minutes  or  more  to  rise  to  their 
working  stage  of  magnetisation. 


LESSON  XXVII. — Electrodynamics. 

331.  Electrodynamics. — In  1821,  almost  immedi- 
ately after  Oerstedt's  discovery  of  the  action  of  a  current 
on  a  magnet,   Ampere  discovered  that  a  current  acts 
upon    another    current,    attracting    it1    or    repelling    it 
according  to  certain   definite  laws.     These  actions  he 
investigated  by  experiment,  and  from  the  experiments 
he  built  up  a  theory  of  the  force  exerted  by  one  current 
on  another.     That   part  of  the  science    which  is   con- 
cerned  with   the   force  which   one  current  exerts  upon 
another  he  tenned  Electrodynamics. 

332.  Laws  of  Parallel  and  Oblique  Circuits. — 
The  following  are  the  laws  discovered  by  Ampere  : — 

1  It  would  be  more  correct  to  speak  of  the  force  as-  acting  on  cf>ndi<ciort 
((inyiug  cu>rentst  than  as  acting  on  the  current?  themselves.  It  is  disputed 
whether  the  current  in  the  conductor  is  attracted;  we  know  only  with 
certainty  that  the  conductor  itself  experiences  a  force.  See,  however. 
Art.  337. 


CHAP,  v.]    ELECTRICITY  AND  MAGNETISM. 


299 


(i.)  Two  parallel  portions  of  a  circuit  attract  one 
another  if  the  currents  in  them  are  flowing  in  the  same 
direction,  and  repel  one  another  if  the  currents  flow  in- 
opposite  directions. 

This  law  is  true  whether  the  parallel  wires  be  parts 
of  two  different  circuits  or  .parts  of  the  same 
circuit.  The  separate  turns  of  a  spiral  coil,  like 
Fig.  ii  8,  for  example,  when  traversed  by  a 
current  attract  one  another  because  the  current 
moves  in  the  same  direction  in  adjacent  parts  of 
the  circuit ;  such  a  coil,  therefore,  shortens  when 
a  current  is  sent  through  it. 

(ii.)  Two  portions  of  circuits  crossing  one  another 
obliquely  attract  one  another  if  both  the  currents  run 
either  towards  or  from  the  point  of  crossing,  a  nd  repel 
one  another  if  one  runs  to  and  the  other  from,  that 
Point. 

Fig.  119  gives  three  cases  of  attraction  and  two  of 
repulsion  that  occur  in  these  laws. 

(iii.)  When  an  element  of  a  circuit  exerts  a  force  on 
another  element 
of  a  circuit,  that 
force  always 
tends  to  urge  the 
latter  in  a  direc- 
tion at  right 
angles  to  its  own 
direction.  Thus, 
in  the  case  of  two 
parallel  circuits,, 
the  force  of  at- 
traction or  repul- 
sion acts  at  right- 


Fig,  ny. 


angles  to  the  currents  themselves. 

An  example  of  laws  ii.  and  iii.  is  afforded  by  the 
case  shown  in  Fig.  120.     Here  two  currents  ab 


300 


ELEMENTARY  LESSONS  ON        [CHAP.  v. 


Flgt  120> 


and  cd  are  movable  round  O  as  a  centre.     There 
will  be  repulsion  between  a  and  d  and  between  c 

and    b,    while    vti    the 

^^  *  '       other   quadrants   there 

will  be  attraction,  a 
attracting  c,  and  b  at- 
tracting d. 

The  foregoing  laws 
may  be  summed  up  in 
one,  by  saying  that  two  portions  of  circuits,  how- 
ever situated,  experience  a  mutual  force  tending 
to  set  them  so  that  their  currents  flow  as  nearly 
,    in  the  same  path  as  possible. 

(iv.)  The  force  exerted  between  two  parallel  portions 
of  circuits  is  proportional  to  the  product  of  the  strengths 
of  the  two  currents,  to  the  length  of  the  portions,  and 
inversely  proportional  to  the  distance  between  them. 

333,  Ampere's  Table. — In  order  to  observe  these 


Fig. 


attractions  and  repulsions,  Ampere  devised  the  piece  of 
apparatus  knowrras  Ampere's  Table,  shown  in  Fig.  121, 


CHAP,  v.]     ELECTRICITY  AND  MAGNETISM.  301 

consisting  of  a  double  supporting  stand,  upon  whicn 
conductors  formed  of  wire,  shaped  in  different  ways,  can 
be  'hung  in  such  a  way  as  to  be  capable  of  rotation. 
In  the  figure  a  simple  loop  is  shown  as  hung  upon  the 
supports.  The  ends  of  the  wires  of  the  movable 
portion  dip  into  two  mercury  cups  so  as  to  ensure  good 
contact.  The  solenoid,  Fig.  1 18,  is  intended  to  be  hung 
upon  the  same  stand. 

By  the  aid  of  this  niece  of  apparatus  Ampere  further 
demonstrated  the  following  points  : — 

(a)  A  circuit  doubled  back  upon  itself,  so  that  the 
current  flows  back  along  a  path  close  to  itself, 
exerts  no  force  upon  external  points. 

(b)  A  circuit  bent  into  zig-zags  or  sinuosities,  pro- 
duces the  same  magnetic  effects  on   a   neigh- 
bouring piece  of  circuit  as  if  it  were  straight. 

(c)  There  is  in  no  case  any  force  tending  to  move  a 
conductor  in  the  direction  of  its  own  length. 

(d)  The  force  between  two  conductors  of  any  form  is 
.he  same,  whatever  the  linear  size  of  the  system, 
provided  the  distances  be  increased  in  the  same 
proportion,  and  *that  the  currents   remain  the 
same  in  strength. 

The  particular  case,  given  in  Fig.  122,  will  show  the 
value  of  these  experiments:  Let  AB  and 'CD  represent 
l  wo  wires  carrying  currents,  lying  neither  parallel  nor  in 
the  same  plane.  *It  follows  from  (£),  that  if  we  replace 
the  portion  PQ  by  the  crooked  wire  PRSQ,  the  force 
will  remain  the  same.  The  portion  PR  is  drawn  verti- 
cally downwards,  and,  as  it  can,  by  (c)y  experience  no 
force  in  the  direction  of  its  length,  this  portion  will 
•  neither  be  attracted  nor  repelled  by  CD.  In  the  portion 
RS  the  current  runs  at  right  angles  to  CD,  and  this 
portion  is  neither  attracted  nor  repelled  by  CD.  In  the 
portion  SQ  the  current  runs  parallel  to  CD,  and  in  the 
same  direction,  and  will  therefore  be  attracted -'down- 


302  •  ELEMENTARY  LESSONS  ON      r  [CHAP.  V. 

wards.  On  the  whole,  therefore,  PQ  will  be  urged  to- 
wards CD.  The  portions  PR  and  RS  will  experience 
forces  of  rotation  hov/ever,  P  being  urged  round  R  as  a 


Fig  122. 

centre  towards  C,  and  R  being  urged  horizontally  round 
S  towards  C.  These  actions  would  tend  to  make  AB 
parallel  with"  CD. 

334.  Ampere's  Theory. — Fronf/.lie  four  preceding 
experimental  data,  Ampere  built  up  an  elaborate  mathe- 
matical theory,  assuming  that,  in  the  case  Of  these  forces 
acting  apparently  at  a  distance  across  empty  space,  the 
action  took  place  in  straight  lines  between  two  points, 
the  total  attraction  being  calculated  as  the  sum  of  the 
separate  attractions  on  all  the  different  parts.  The 
researches  of 'Faraday  have,  however,  led  to  other  views, 
and  we  now  regard  the  mutual  attractions  and  repulsions 
of  currents  as  being  due  to  actions  taking  place  in  the 
medium  which  fills  the  space  around  and  between  the 
conductors.  That  space  we  regard  rather  as  bejng  full 
of  curving  ~"  lines  of  force."  Every  wire  carrying  a 
current  has  a  magnetic  field,  like  that  of  Fig.  85,  sur- 
rounding it ;  and  every  closed  circuit  acts  as  a  magnetic 
shell:  Hence  all  these  electrodynamic  actions  are 
capable  of  being  regarded  as  magnetic  actions,  and  they 
can  be  predicted  beforehand  for  any  particular  case  on 
that  supposition.  Thus,  the  author  of  these  Lessons 


CHAP,  v.]    ELECTRICITY  AND  MAGNETISM.  303 

has  shown1  that  in  the  case  of  two  parallel  concurrent 
circuits  the  "  lines  of  force  "  due  to  the  two  systems 
run  into  one  another,  embracing  both  circuits,  while  in 
the  case  of  two  parallel  and  non-concurrent  circuits  the 
"  lines  of  force  "  due  to  the  two  currents  indicate  mutual 
repulsion.  The  theory  of  Maxwell,  that  a  voltaic  circuit 
acts  like  a  magnetic  shell  (a  direct  deduction  from  Fara- 
day's work),  is  in  practice  a  more  fruitful  conception  than 
that  of  Ampere.  On  Maxwell's  theory  two  circuits  will 
tend,  like  two  magnetic  shells,  to  move  so  as  to  include 
as  many  of  one  another's"  Alines  of  force  "  as  possible 
(Art.  193  and  320).  This  will  be  the  case  when  they 
coincide  as  nearly  as  possible  ;  i.e.,  when  the  two  wires 
are  parallel  in  every  part,  and  when  the  currents  run 
round  in  the  same  direction.  In  fact,  all  the  electro- 
dynamic  laws  of  parallel  and  oblique  circuits  can  be 
deduced  from  Maxwell's  theory  in  the  simplest  manner. 
An  interesting  experiment,  showing  an  apparent 
mutual  self-repulsion  between  contiguous  portions  of  the 
circuit,  was  devised  by  Ampere.  A  trough  divided  by 
a  partition  into  two  parts,  and  made  of  non-conducting 
materials,  is  filled  with _ mercury.  Upon  .it  floats  a 


Fig-  123- 

metallic  bridge  formed  of  a  bent  wire,  of  the  form  shown 
in  Fig.  123,  or  consisting  of  a  glass  tube  filled  siphon- 
wise  with  mercury.  When  a  current  is  sent  through 
the  floating  conductor  from  X  ove.r  MN,  and  out  at 

\.Philosophical Magazine,  November  1878}  P-.34.8. 


304  ELEMENTARY  LESSONS  ON        [CHAP.  v. 

Y,  the  floating  bridge  is  observed  to  move  so  as  to 
increase  the  length  of  the  circuit.  But  Maxwell  has 
shown  that  the  true  explanation  depends  upon  the  self- 
induction  (Ait.  404)  of  the  two  parallel  portions  of  the 
floating  conductor,  and  that  the  force  would  be  diminished 
indefinitely  if  the  two  parallel  parts  could  be  made  to 
lie  quite  close  to  one  another. 

335.  Electromagnetic  Rotations.  —  Continuous 
rotation  can  be  produced  between  a  magnet  and  a 
circuit,  or  between  two  parts  of  one  circuit,  provided 
that  one  part  of  the  circuit  can  move  while  another  part 
remains  fixed,  or  that  the  current  in  one  part  can  be 
leversed.  The  latter  device  is  adopted  in  the  construc- 
tion of  the  electromagnetic  engines  described  in  Art.  375  ; 
the  former  alternative  is  applied  in  a  good  many  interest- 
ing pieces  of  apparatus  for  showing  rotations,  a  sliding- 
contact  being  made  between  one  part  of  the  circuit  and 
another.  Several  different  forms  of  rotation-apparatus 
n  ere  devised  by  Faraday  and  by  Ampere.  One  of  the 
•simplest  of  these  is  shown  in  Fig.  124,  in  which  a 


Fie.  124. 


current  rising  through  a  and  passing  through  the  lightly 
pivoted  wire  b  V  in  either  direction,  passes  down  into 
a  circular  trough  containing  mercury.  The  trough  is 
made  of  copper,  and  is  connected  with  a  wire  which  is 
also  wound  in  a  coil  round  the  outside  of  the  trough, 


CHAP,  v.]     ELECTRICITY  AND  MAGNETISM.  305 

and  which  forms  part  of  the  circuit.  The  arrows  show 
the  direction  of  the  currents.  The  currents  in  the 
circular  coils  constitute  a  magnetic  shell,  whose  N.-seek- 
ing  face  is  uppermost.  The  lines  of  force  due  to  this 
shell  therefore  run  vertically  in  an  upward  direction. 
According  to  the  converse  to  Ampere's  Rule  (Art.  186), 
a  man  swimming  in  one  of  the  horizontal  branches 
from  the  centre  a  outwards,  and  looking  along  the  lines 
of  force,  i.e.  turned  on  to  his  back,  so  as  to  look  upwards, 
will  be  carried,  along  with  the  conductor,  toward  his  left 
hand.  And  the  pivoted  conductor  as  seen  from  above 
will  rotate  continuously  in  the  same  sense  as  the  hands 
of  a  clock  around  the  centre  a.  A  pole  of  a  magnet 
can  also  be  made  to  rotate  round  a  current ;  and  if  a 
vertical  magnet  be  pivoted  so  as  to  turn  around  its 
own  axis  it  will  rotate  when  a  current  is  led  into  its 
middle  region  and  out  at  either  end.  If  the  current  is 
led  in  at  one  end  and  out  at  the  other  there  will  be  no 
rotation,  since  the  two  poles  will  thus  be  urged  to  rotate 
in  opposite  ways,  which  is  impossible.  Liquid  con- 
ductors too  can  exhibit  electromagnetic  rotations.  Let  a 
•cylindrical  metallic  vessel  connected  to  one  pole  of  a 
battery  be  filled  with  mercury  or  dilute  acid,  and  let 
a  wire  from  the  other  pole  dip  into  its  middle,  so  that 
a  current  may  flow  radially  from  the  centre  to  the 
circumference,  or  vice  versa;  then,  if  this  be  placed 
upon  the  pole  of  a  powerful  magnet,  or  if  a  magnet 
be  held  vertically  over  it,  the  liquid  may  be  seen  to 
rotate. 

336.  Electrodynamometer. — Weber  devised  an 
instrument  known  as  an  eleclrodynamometer  for  measur- 
ing the  strength  of  currents  by  means  of  the  electro- 
dynamic  action  of  one  part  of  the  circuit  upon  another  part. 
It  is  in  fact  a  sort  of  galvanometer,  in  which,  instead  of 
a  needle,  there  is  a  small  coil  suspended.  One  form  of 
this  instrument,  in  which  both  the  large  outer  and  small 
inner  coils  consist  of  two  parallel  coils  of  many  turns,  is 

x 


ELEMENTARY  LESSONS  ON        [CHAP.  v. 


shown  in  Fig.  125.*  The  inner  coil  CD  is  suspended  with 
its  axis  at  right  angles  to  that  of  the  outer  coils  AA,  BB, 
and  is  supported  bifilarly  (see  Art.  118)  by  two  fine 

metal  wires.  If 
one  current  flows 
round  both  coils  in 
either  direction  the 
inner  bobbin  tends 
to  turn  and  set  its 
coils  parallel  to 
the  outer  coils ; 
the  sine  of  the 
angle  through 
which  the  sus- 
pending wires  are 
twisted  being  pro- 
portional to  the 
i  square  of  the 
1  strength  of  the  cur- 
rent. The  chief 
advantage  of  this 
instrument  over  a 

Fig.  125.  . 

galvanometer    is, 

that  it  may  be  used  for  lnduction:currents  in  which  there 
are  very  rapid  alternations, — a  Current  in  one  direction 
being  followed  by  a  reverse  current,  perhaps  thousands  of 
times  in  a  minute.  Such  currents  hardly  affect  a  galvano- 
meter needle  at  all,  because  of  the  slowness  of  its  swing. 
Siemens  employs  an  electrodynamometer  with  coils 
made  of  very  thick  wire  for  the  absolute  measurement 
of  strong  currents,  such  as  are  used  in  producing 
electric  light.  If  is  possible  also  to  use  an  electro- 
dynamometer  as  a  "Power-meter"  to  measure  the 
electric  horse  power  evolved  by  a  battery  or  consumed 
in  an  electric  lamp  or  machine.  -In  this  case  the  whole 
current  is  sent  through  a  fixed  coil  of  thick  wire,  while 
the  movable  coil,  made  of  many  turns  of  thin  wire,  is 


CHAP,  v.]      ELECTRICITY  AND  MAGNETISM.        306* 

connected  as  a  shunt  across  the  terminals  of  the  lamp 
or  machine  being  thus  traversed  by  a  current  proportional 
to  the  difference  of  potential  between  those  points  (see 
Art.  360  d}.  The  sine  of  the  angle  of  deflection  will 
be  proportional  to  the  product  of  the  two  currents,  and 
therefore,  to  the  product  of  the  whole  current  into  the 
difference  of  potential  (see  Art.  378  bis). 

337.  Electromagnetic  Actions  of  Convection 
Currents. — According  to  Faraday  a  stream  of  particles 
charged  with  electricity  acts  magnetically  like  a  true 
conduction-current.  This  was  first  proved  in  1876  by 
Rowland,  who  found  a  charged  disc  rotated  rapidly  to 
act  upon  a  magnet  as  a  feeble  circular  current  would  do. 
Convection  currents,  consisting  of  streams  of  electrified 
particles,  are  also  acted  upon  by  magnets.  The  con- 
vective  discharges  in  vacuum-tubes  (Art  292)  can  be 
drawn  aside  by  a  magnet,  or  caused  to  rotate  around 
a  magnet-pole.  The  "  brush  "  discharge  when  taking 
place  in  a  strong  magnetic  field  is  twisted.  The  voltaic 
arc  (Art.  371)  also  behaves  like  a  flexible  conductor, 
and  can  be  attracted  or  repelled  by  a  magnet.  Two 
stationary  positively  electrified  particles  repel,  one 
another,  but  two  parallel  currents  attract  one  another 
(Art.  332),  and  if  electrified  particles  flowing  along  act 
like  currents,  there  should  be  an  (electromagnetic)  attrac- 
tion between  two  electrified  particles  moving  along 
side  by  side  through  space.  According  to  Maxwell's 
theory  (Art.  390)  the  electrostatic  repulsion  will  be  just 
equal  to  the  electromagnetic  attraction  when  the  particles 
move  with  a  velocity  equal  to  the  velocity  of  light. 

Quite  recently  Hall  has  discovered  that  when  a 
powerful  magnet  is  made  to  act  upon  a  current  flowing 
along  in  a  strip  of  very  thin  metal,  the  equipotential 
lines  are  no  longer  at  right-angles  to  the  lines  of  flow  of 
the  current  in  the  strip.  This  action  appears  to  be 
connected  with  the  magnetic  rotation  of  polarized  light 
(Art.  387),  the  co.-efficient  of  this  transverse  thrust  of 


3o6r  ELEMENTARY  LESSONS  ON          CHAP.  v. 

the  magnetic  field  on  the  current  being  feebly  -f-  in  gold, 
strongly  +  in  bismuth,  and  -  in  iron,  and  immensely 
strong  negatively  in  tellurium.  It  was  shown  by  the 
author,  and  about  the  same  time  by  Righi,  that  those 
metals  which  manifest  the  Hall  effect  undergo  a  change 
in  their  electric  resistance  when  placed  in  the  magnetic 
field. 

338.  Ampere's  Theory  of  Magnetism. — Am- 
pere, finding  that  solenoids  (such  as  Fig.  1 1 8)  act  pre- 
cisely as  magnets,  conceived  that  all  magnets  are  simply 
collections  Qf^  currents,  or  that,  around  every  individual 
molecule  of  a  magnet  an  electric  current  is  ceaselessly 
circulating.  We  know  that  such  currents  could  not 
flow  perpetually  if  there  were  any  resistance  to  them, 
and  we  know  that  there  is  resistance  when  electricity 
flows  from  one  molecule  to  another.  As  we  know 
nothing  about  the  interior  of  molecules  themselves,  we 
cannot  assert  that  Ampere's  supposition  is  impossible. 
Since  a  whirlpool  of  electricity  acts  like  a  magnet. 
there  seems  indeed  reason  to  think  that  magnets  may 
be  merely  made  up  of  rotating  portions  of  electrified 
matter. 


CHAP,  v.]      ELECTRICITY  AND  MAGNETISM.         306^ 


LESSON  XXVIII.  —  Diamagnetism. 

339.  Diamagnetic  Experiments.  —  In  1778 
Brugmans  of  Leyden  observed  that  when  a  lump  of 
bismuth  was  held  near  either  pole  of  a  magnet  needle  it 
repelled  it.  In  1827  Le  Baillif  and  Becquerel  observed 
that  the  metal  antimony  also  could  repel  and  be  repelled 
by  the  pole  of  a  magnet.  In  1845  Faraday,  using  power- 
ful electromagnets,  examined  the  magnetic  properties 
of  a  large  number  of  substances,  and  found  that  whilst  a 
great  many  are,  like  iron,  attracted  to  a  magnet,  others 
are  feebly  repelled.  To  distinguish  between  these  two 
classes  of  bodies,  he  termed  those  which  are  attracted 
paramagnetic,1  and  those  which  are  repelled  diamag- 
netic.  The  property  of  being  thus  repelled  from  a  magnet 
he  termed  diamagnetism. 

Faraday's  method  of  experiment  consisted  in  suspend- 
ing a  small  bar  of  the  substance  in  a  powerful  magnetic 
field  between  the  two  poles  of 
an  electromagnet,  and  observing 
whether  the  small  bar  was  at- 
tracted into  an  axial  position,  as 
in  Fig.  126,  with  its  length  along 
the  line  joining  the  two  poles,  or 
whether  it  was  repelled  into  an 
equatorial  position,  at  right 
angles  to  the  line  joining  the  poles, 
across  the  lines  of  force  of  the 
field,  as  is  shown  by  the  position 
of  the  small  bar  in  Fig  127,  sus- 
pended between  the  poles  of  an  electromagnet  con- 
structed on  Ruhmkorff's  pattern. 


Fig.  126. 


1  Or  simply  "  magnetic."  Some  authorities  use  the  term  "  ferro- 
magnetic." Sidero-magnetic  would  be  less  objectionable  than  this  hybrid 
word. 


30&? 


ELEMENTARY  LESSONS  ON        [CHAP,  v: 


CS 


Fig.  127. 

The  following  are  the  principal  substances  examined 
by  the  method  : — 


Paramagnetic. 


Iron. 

Nickel. 

Cobalt. 

Manganese. 

Chromium. 

Cerium. 

Titanium. 

Platinum.1 

Many  ores  and  salts 
containing  the 
above  metals. 

Oxygen  gas. 


Diamagnetic. 


Bismuth. 

Phosphorus 

Antimony. 

Zinc. 

Mercury. 

Lead. 

Silver. 

Copper. 

Gold. 

Water. 

Alcohol. 

Tellurium. 

Selenium. 

Sulphur. 

Thallium. 

Hydrogen  gas. 

Air. 


Chemically  pure  Platinum  is  diawa^netic,  according  to  Wiedemann, 


CHAP,  v.1     ELECTRICITY  AND  MAGNETISM.         3067 

Liquids  were  placed  in  glass  vessels  and  suspended 
between  the  poles  of  the  electromagnet.  Almost  all 
liquids  are  diamagnetic,  except  solutions  of  salts  of  the 
magnetic  metals,  some  of  which  are  feebly  magnetic ; 
but  blood  is  diamagnetic  though  it  contains  iron.-  To 
examine  gases  bubbles  are  blown  with  them,  and  watched 
as  to  whether  they  were  drawn  into  or  pushed  out  of 
the  field.  Oxygen  gas  was  found  to  be  magnetic ;  ozone 
has  recently  been  found  to  be  still  more  strongly  so. 

340.  Quantitative    Results. — The    diamagnetic 
properties  of  substances  may  be  numerically  expressed 
in    terms    of  their   susceptibility   or   their  permeability 
(Art.  3 1 3).     For  diamagnetic  bodies  the  susceptibility  k 
is  negative,  and  therefore  the  permeability  (/i  =  I  +  ^irk) 
is  less   than    unity.      For  bismuth  the  value  of  k  is 
—  0-0000025  according  to  Maxwell.     The  repulsion  of 
bismuth  is  immensely  feebler  than  the  attraction  of  iron. 
Pliicker  compared  the  magnetic  powers  of  equal  weights 
of  substances,  and  reckoning  that  of  iron  as  one  million, 
he  found  the  following  values  for  the  "specific  mag- 
netism "  of  bodies  : — 

Iron  +  1,000,000 

Lodestone  Ore  +  402,270 

Ferric  Sulphate  +  I, no 

Ferrose  Sulphate  +  780 

Water  _  7-8 

Bismuth  -  23  '6 

341.  Apparent    Diamagnetism    due    to    sur- 
rounding Medium. — It  is  found  that  feebly  magnetic 
bodies  behave  as  if  they  were  diamagnetic  when  sus- 
pended in  a  more  highly  magnetic  fluid.     A  small  glass 
tube  filled  with  a  weak  solution  of  ferric  chloride,  when 
suspended  in  air  between  the  poles  of  an  electromagnet 
points   axially,   or  is  paramagnetic ;   but   if  it   be   sur- 
rounded by  a  stronger  (and  therefore  more  magnetic) 
solution  of  the  same  substance,  it  points  equatorially,  and 
is  apparently  repelled  like  diamagnetic  bodies.     All  that 


306^  "ELEMENTARY  LESSONS  ON       [CHAP.  v. 

the  equatorial  pointing  of  a  body  proves  then  is,  that  it  is 
less  magnetic  than  the  medium  that  fills  the  surrounding 
space.  A  balloon,  though  it  possesses  mass  and  weight, 
rises  through  the  air  in  obedience  to  the  law  of  gravity, 
because  the  medium  surrounding  it  is  more  attracted 
than  it  is.  But  it  is  found  that  diamagnetic  repulsion 
takes  place  even  in  a  vacuum :  hence  it  would  appear 
that  space  itself1  is  more  magnetic  than  the  substances 
classed  as  diamagnetic. 

342.  Diamagnetic  Polarity. — At  one  time  Faraday 
thought  that  diamagnetic  repulsion  could  be  explained 
on  the  supposition  that  there  existed  a  "diamagnetic 
polarity  "  the  reverse  of  the  ordinary  magnetic  polarity. 
According  to  this  view,  which,  however,  Faraday  him- 
self quite  abandoned,  a  magnet,  when  its  N.  pole  is  pre- 
sented to  the  end  of  a  bar  of  bismuth,  -induces  in  that 
end  a  N.  pole  (the  reverse  of  what  it  would  induce  in  a 
bar  of  iron  or  other  magnetic  metal),  and  therefore  repels 
it.  Weber  adopted  jthis  view,  and  Tyndall  warmly 
advocated  it,  especially  after  discovering  that  the  repel- 
ling diamagnetic  'force  varies  as  the  square  of  the 
magnetic  power  employed,  a  law  which  is  the  counter- 
part of  the  law  (Art.  328)  of  attraction  due  to  induction. 
Many  experiments  have  been  made  to  establish  this 
view ;  and  some  have  even  imagined  that-  when  a 
diamagnetic  bar  lies  equatorially  across  a  field  of  force, 
its  east  and  west  poles  possess  different  properties.  The 
experiments  named  in  the  preceding  paragraph  suggest, 
however,  an  explanation  less  difficult  to  reconcile  with 
the  facts.  There  can  be  no  doubt  that  the  phenomenon 
is  due  to  magnetic  induction :  and  it  has  been  pointed 
out  (Art.  89)  that  the  amount  of  induction  which  goes 
on  in  a  medium  depends  upon  the  magnetic  inductive 
capacity  (or  "permeability")  of  that  medium.  Now, 
permeability  expresses  the  number  of  magnetic  lines 
induced  in  the  medium  for  every  line  pf  magnetising  force 

1  0«*.  possibly,  the  "  aether  "  filling  all  space. 


CHAP,  v  ••     ELECTRICITY  AND  MAGNETISM.,         306;* 

applied.  A  certain  magnetising  force  applied  to  a  space 
containing  air  or  vacuum  would  induce  a  certain  number 
of  magnetic  lines  through  it.  If,  however,  the  space  con- 
sidered were  occupied  by  bismuth,  the  same  magnetising- 
force  would  induce  in  the  bismuth  fewer  "lines  of  induc- 
tion "  than  in  vacuum.  But  those  lines  which  were  induced 
would  still  run  in  the  same  general  direction  as  in  the 
vacuum ;  not  in  the  opposite  direction^  as  Weber  and 
Tyndall  maintain.  The  result  of  there  being  a  less  in- 
duction through  diamagnetic  substances  can  be  shown 
to  be  that  such  substances  will  be  urged  from  places 
where  the  magnetic  force  is  strong,'  to  places  where  it  is 
weaker.  _  This  is  why  a  ball  of  bismuth  moves  away 
from  a  magnet,  and  why  a  little  bar  of  bismuth  between 
the  conical  poles  of  the  electro-magnet  (Fig.  127)  turns 
equatorially  so  as  to  put  its  ends  into  the  regions  that 
are  magnetically  weaker.  There  is  no  reason  to  doubt 
that  in  a  magnetic  field  of  uniform  strength  a  bar  ol 
bismuth  would  point  along  the  lines  of  i  duction. 

343.  Magne  -  Crystailic  Action.  —  In  1822 
Poisson  predicted  that  a  body  possessing  crystalline 
structure  would,  if  magnetic  at  all,  have  different 
magnetic  powers  in  different  directions.  In  1847 
Pliicker  discovered  that  a  piece  of  tourmaline,  which 
is  itself  feebly  paramagnetic,  behaved  as  a  diamagnetic 
body,  when  so  hung  that  the  axis  of  the  crystal  was 
horizontal.  Faraday,  repeating  the  experiment  with  a 
crystal  of  bismuth,  found  that  it  tended  to  point  with 
its  axis  of  crystallisation  along  the  lines  of  the  field 
axially.  The  magnetic  force  acting  thus  upon  crystals 
by  virtue  of  their  possessing  a  certain  structure  he 
named  magne-crystallic  force.  Pliicker  endeavoured  to 
connect  the  magne-crystallic  behaviour  of  crystals  with 
their  optical  behaviour,  giving  the  following  law :  there 
will  be  either  repulsion  or  attraction  of  the  optic  axis 
(or,  in  the  case  of  bi-axial  crystals,  of  both  optic  axes) 
by  the  poles  of  a  magnet ;  and  if  the  crystal  is  a 


306*  ELEMENTARY  LESSONS  ON        [CHAP.  V. 

"  negative  "  one  (i.e.  optically  negative,  having  an  extra- 
ordinary index  of  refraction  /ess  than  its  ordinary  index), 
there  will  be  icpulsion,  if  a  "positive"  one,  there  will 
be  attraction.  Tyndall  has  endeavoured  to  show  that 
this  law  is  insufficient  in  not  taking  into  account  the 
paramagnetic  or  diamagnetic  powers  of  the  substance  as 
a  \\hole.  He  finds  that  the  magne-crystallic  axis  of 
bodies  is  in  general  an  axis  of  greatest  density,  and  that 
if  the  Mfitr  itself  be  paramagnetic  this  axis  'will  point 
axially;  if  diamagnetic^  sqitatorially.  In  bodies  \\hich, 
like  slate  and  many  crystals,  possess  cleavage,  the  planes 
of  cleavage  are  usually  at  right  angles  to  the  magne- 
crystallic  axis. 

344.  Diainagnetism  of  Flames. — In  1847  Ban- 
calari  discovered  that  flames  are  repelled  from  the  axial 
line  joining  the  poles  of  an  electromagnet.  Faraday 
showed  that  all  kinds  of  flames,  as  well  as  ascending 
streams  of  hot  air  and  of  smoke,  are  acted  on  by  the 
magnet  and  tend  to  nune  from  places  \\here  the  mag- 
netic forces  are  stiong  to  those  where  they  are  weaker. 
Gases  (except  oxygen  and  ozone),  and  hot  gases  especi-- 
ally,  are  feebly  diamagnetic.  But  the  active  repulsion 
and  turning  aside  of  flames  may  possibly  be  in  part 
due  to  an  electromagnetic  action  like  that  which  the 
magnet  exercises  on  the  convection-current  of  the  voltaic 
arc  and  on  other  convection-currents.  The  electric  pro- 
perties of  flame  are  mentioned  in  Arts.  7  and  291. 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  307 


CHAPTER  VI. 
MEASUREMENT  OF  CURRENTS,  ETC. 

LESSON  XXIX. — Ohtrfs  Law  and  its  Consequences. 

345.  In  Art.  180  the  important  law  of  Ohm  was 
stated  in  the  following  terms  :  —  The  strength  of  the 
current  varies  directly  as  the  electromotive -force^  and  in- 
versely as  the  (total)  rest  stance  of  the  circuit. 

Using  the  units  adopted  by  practical  electricians,  and 
explained  in  Art.  323,  we  may  now  restate  Ohm's  law  in 
the  following  definite  manner  : — The  number  of  amperes 
of  current  flowing  through  a  circuit  is  equal  to  the  number 
of  volts  of  electromotive-force  divided  by  the  number  of 
ohms  of  resistance  in  the  entire  circuit.  Ort 

Electromotive-force 


Current  — - 


Resistance 


c  =- 

R* 

In  practice,  however,  the  matter  is  not  quite  so  simple, 
for  if  a  number  of  cells  are  used  and  the  circuit  be  made 
up  of  a  number  of  different  parts  through  all  of  which 
the  current  must  flow,  we  have  to  take  into  account  not 
only  the  electromotive-forces  of  the  cells,  but  their  resist- 
tances,  and  the  resistance  of  all  the  parts  of  the  circuit. 
For  example,  the  current  may  flow  from  the  zinc  plate  of 
the  first  cell  through  the  liquid  to  the  copper  (or  carbon) 


3o8  ELEMENT          LESSONS  ON       (CHAP,  vi, 

plate,  then  through  a  connecting  wire  or  screw  to  the  next 
cell,  through  its  liquid,  through  the  connecting  screws  and 
liquids  of  the  rest  of  the  cells,  then  through  a  wire  to  a 
galvanometer,  then  through  the  coils  of  the  galvanometer, 
then  perhaps  through  an  electrolytic  cell,  and  finally 
through  a  return  wire  to  the  zinc  pole  of  the  battery  In 
this  case  there  are  a  number  of  separate  electromotive-forces 
all  tending  to  produce  a  flow,  and  a  number  of  different 
resistances,  each  impeding  the  flow  and  adding  to  the 
total  resistance.  If  in  such  a  case  we  knew  the  separate 
values  of  all  the  different  electromotive- forces  and  all  the 
different  resistances  we  could  calculate  what  the  current 
would  be,  for  it  would  have  the  value, 


Total  electromotive-force 
~  Total  resistance 

If  any  one  of  the  cells  were  set  wrong  way-  round  its 
electromotive-force  would  oppose  that  of  the  other  cells  ; 
an  opposing  electromotive-force  must  therefore  be  sub- 
tracted, or  reckoned  as  negative  hi  the  algebraic  sum. 
The  "polarisation"  (Arts.  163  and  413)  which  occurs 
in  battery  cells  and  in  electrolytic  cells  after  working  for 
some  time  is  an  opposing  electromotive  -  force,  and 
diminishes  the  total  of  the  electromotive -forces  in  the 
circuit.  So,  also,  the  induced  back-current  which  is  set 
up  when  a  current  from  a  battery  drives  a  magneto- 
electric  engine  (Art.  377)  reduces  the  strength  of  the 
working  current. 

346.  Conductivity  and  Resistance. —The  term 
conductivity  is  sometimes  used  as  the  inverse  of 

resistance ;  and  the  reciprocal  -  represents  the  con- 
ductivity of  a  conductor  whose  resistance  is  r  ohms.  In 
practice,  however,  it  is  more  usual  to  speak  of  the 
rtsisfancfs  of  conductors-  than  of  their  conductivities. 


CHAP.  vi.  1-  ELECTRICITY  AND  MAGNETISM.  309 

347.  Laws  of  Resistance. — Resistances  in  a  cir- 
cuit may  be  of  two  kinds— -first  ^  the  resistances  of  the 
conductors  themselves  ;  second,  the  resistances  due  to 
impei-fect  contact  at  points.  The  latter  kind  of  resistance 
is  affected  by-  pressure,  for  when  the  surfaces  of  two 
conductors  are  brought  into  more  intimate  contact  with 
one  another,  { the'  current  passes  more  freely  from  one 
conductor  to  the  other.  The  contact-resistance  of  two 
copper  conductors  may  vary  from  infinity  down  to  a 
small  fraction  of  an  ohm,  according  to  the  pressure. 
The  variation  of  resistance  at  a  point  of  imperfect  con- 
tact is  utilised  in  Telephone  Transmitters  (Arts.  434, 
436).  The  following  are  the  laws  of  the  resistance  of 
conductors  : — 

i.  The  resistance  of  a  conducting  "wire  is  proportional 
to  its  length.  If  the  resistance  of  a  mile  of 
telegraph  wire  be  13  ohms,  that  of  fifty  miles 
will  be  5ox  13  =  650  ohms. 

ii.  The  resistance  of  a  conducting  wire  is  inversely 
proportional  to  the  area  of  its  cross  section,  and 
therefore  in  the  usual  round  wires  is  inversely 
proportional  to  the  square  of  Us  diameter.  Ordi- 
nary telegraph  wire  is  about  $th  of  an  inch  thick  ; 
a  wire  twice  as  thick  would  conduct  four  times  as 
well,  having  four  times  the  area  of  cross  section  : 
hence  an  equal  length  of  it  would  have  only  £th 
the  resistance. 

iii.  The  resistance  oj  a  conducting  wire  oj  given  length 
and  thickness  depend*  upon  the  material  of  which 
it  is  made, — that  is  to  say,  upon  the  specific 
resistance  of  the  material. 

348.  Specific  Resistance. — The  specific  resistance 
of  a  substance  is  best  stated  as  the  resistance  in 
"absolute"  C.G.S.  units  (i.e.  in  thousand  millionths  of 
an  ohm)  of  a  centimetre  cube  of  the  substance.  The 
following  Table  also  gives  the  relative  conductivity  wheu 
that  of  silver  is  taken  as  I  oo. 


ELEMENTARY  LESSONS  ON       [CHAP.  vi. 


TABLE    OF    SPECIFIC    RESISTANCE. 


Substance. 

Specific  Resistance. 

Relative  Conductivity. 

Metals. 

Silver 

1,609 

IOO 

Copper 

1,642 

96 

Gold 

2,154 

74 

Iron  (soft 

9,827 

16 

Lead 

19,847 

8 

German  Silver 

2I,I7O 

7'5 

Mercury  (liquid) 

96,146 

1-6 

Selenium  (annealed 

6  x   io13 

i 

40iOOO.000.000 

Liquids. 

Pure  Water  ) 
at  22°c     ) 
Dilute  H2SO4  ) 
(^a  acid)      > 

7-18     x  io10 
•332  x  iow 

less  than  cite 
millionth  part. 

Dilute  H2SO4  | 
(i  acid)      j 

•126  x   io10 

Insulators. 

Glass  (at  2OO°c) 

2'27    X    IO16 

less  than  one 

Guttapercha 
(at  20  'c) 

3*5     x   Io23 

billionth. 

It  is  found  that  those  substances  that  possess  a  high 
conducting  power  for  electricity  are  also  the  best  con- 
ductors of  heat.  Liquids  are  worse  conductors  than  the 
metals,  and  gases  are  perfect  non-conductors,  except 
when  so  rarefied  as  to  admit  of  discharge  by  convection 
through  them  (Art.  283). 

349.  Effects  of  Heat  on  Resistance. — Changes 
of  temperature '  affect  temporarily  the  conducting  power 
of  metals.  Forbes  found  the  resistance  of  iron  to 
increase  -considerably  as  the  temperature  is  raided.  The 
resistances  of  .copper  and  lead  also  increase,  while  that 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  3n 

of  carbon  appears  on  the  other  hand  to  diminish  on 
heating.  German-silver  and  other  alloys  do  not  show 
so  much  change,  hence  they  are  used  in  making  standard 
resistance-coils.  Those  liquids  which  only  conduct  by 
be.ng  electrolysed  (Art.  205),  conduct  better  as  the 
temperature  rises.  The  effect  of  light  in  varying  the 
resistance  of  selenium  is  stated  in  Art.  389. 

350.  Typical  Circuit. — Let  us  consider  the  typical 
case  of  the  circuit  shown 
in  Fig.  128,  in  which  a 
battery,  ZC,  is  joined  up 
in  circuit  with  a  galvano- 
meter by  means  of  wires 
whose  resistance  is  R. 
The  total  electromotive- 
force  of  the  battery  we 
will  call  E,  and  the  total  *'«•  I28- 

internal  resistance  of  the  liquids  in  the  cells  r.  The 
resistance  of  the  galvanometer  coils  may  be  called  G. 
Then,  by  Ohm's  law  : — 

C-— 5 • 

R  +  r  +  G 

The  internal  resistance  r  of  the  liquids  of  the  battery 
bears  a  very  important  relation  to  the  external  resistance 
of  the  circuit  (including  R  and  G),  for  on"  this  relation 
depends  the  best  way  of  arranging  the  battery  cells 
for  any  particular  purpose.  Suppose,  for  example, 
that  we  have  a  battery  of  50  small  DanielPs  cells  at 
our  disposal,  of  which  we  may  reckon  the  electro- 
motive-force as  one  volt  (or  more  accurately,  1-079  volt) 
each,  and  each  having  an  internal  resistance  of  two 
ohms.  If  we  have  to  use  these  cells  on  a  circuit  where 
there  is  already  of  necessity  a  high  resistance,  we  should 
couple  them  up  "  in  simple  series "  rather  than  in 
parallel  branches  of  a  compound  circuit.  For,  suppos- 
ing we  have  to  send  our  current  through  a  line  of 
telegraph  100  miles  long,  the  external  resistance  R 


JI2    —  —      ELEMENTARY  LESSONS  ON       [CHAP.  vi. 

be  (reckoning  13  ohms  to  the  mile  of  wire)  at  leas' 
1300  ohms.  Through  this  resistance  a  single  such  eel 
would  give  a  current  of  less  than  one  milli-ampere,  for 
here  E  =  I,  R  =  1300,  r  —  2,  and  therefore 

C  =  p     •-   =   — ^-r—    =  -i-  of  an  ampere,  a  current  far 

R  +  r          1300  +  2  1302 

too  weak  to  work  a  telegraph  instrument. 

With  fifty  such  cells  in  series  we  should  have  E  =  50, 
r  =  100,  and  then 

C  =  — —. =  -^-  =  -^  of  an  ampere,  or  over  3  5  milli- 

1300  +   100  1400  30  J  J 

amperes.  In  telegraph  work,  where  the  instruments 
require  a  current  of  5  to  I  o  milli-amperes  to*  work  them, 
it  is  usual  to  reckon  an  additional  Daniell's  cell  for  every 
5  miles  of  line,  each  instrument  in  the  circuit  being 
counted  as  having  as  great  a  resistance  as  10  miles  of 
wire. 

If,  however,  the  resistance  of  the  external  circuit  be 
small,  such  arrangements  must  be  made  as  will  keep  the 
total  internal  resistance  of  the  battery  small.  Suppose, 
for  example,  we  wish  merely  to  heat  a  small  piece  of 
platinum  wire  to  redness,  and  have  stout  copper  wires 
to  connect  it  with  the  battery.  Here  the  external  resist- 
ance may  possibly  not  be  as  much  as  one  ohm.  In  that 
case  a  single  cell  would  give  a  current  of  \  of  an  ampere 
(or  333  milli-amperes)  through  the  wire,  for  here  E  =  I, 
R  =  I,  and  r  =  2.  But  ten  cells  would  only  give  half 
as  much  again,  or  476  milli-amperes,  and  fifty  cells  only 
495  milli-amperes,  and  with  an  infinite  number  of  such 
cells  in  series  the  current  could  not  possibly  be  more 
than  500  milli-amperes,  because  every  cell,  though  it  adds 
i  to  E,  adds  2  to  R.  It  is  clear  then  that  though  link- 
ing many  cells  in  series  is  of  advantage  where  there  is 
the  resistance  of  a  long  line  of  wire  to  be  overcome,  yet 
where  the  external  resistance  is  small  the  practical  advan 
tage  of  adding  cells  in  series  soon  reaches  a  limit. 

But  suppose  in  this  second  case,  where  the  external 
resistance  of  the   circuit  is  small,  we  reduce  also  the 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  313 

internal  resistance  of  our  battery  by  linking  cells  to- 
gether in  parallel  branches  of  a  compound  circuit,  join- 
ing several  zincs  of  several  cells  together,  and  joining 
also  their  copper  poles  together  (as  suggested  in  Art. 
181),  a  different  and  better  result  is  attained.  Suppose 
j  we  thus  join  up  four  cells.  Their  electromotive-force 
'  will  be  no  more,  it  is  true,  than  that  of  one  cell,  but 
their  resistance  will  be  but  £  of  one  such  cell,  >r  |  an 
ohm.  These  four  cells  would  give  a  current  of  666 
milli-amperes  through  an  external  resistance  of  I  ohm, 
for  if  E  =  i,  R  =  i,  and  the  internal  resistance  be  ^ 
of  r,  or  =  £,  then 

C  =  R^  r  =  §  of  an  ampere,  or  666  milli-amperes. 

351.  Best  Grouping  of  Cells.  —  It  is  at  once 
evident  that  if  we  arrange  the  cells  of  a  battery  in  « 
files  of  m  cells  in  series  in  each  file  (there  being  m  x  n 
similar  cells  altogether),  the  electromotive-force  of  each 
file  will  be  m  times  the  electromotive  -force  E  of  each 
cell,  or  wE  ;  and  the  resistance  of  each  file  will  be  m 
times  the  resistance  r  of  each  cell,  or  mr.  But  there 
being  n  files  in  parallel  branches  the  whole  internal 
resistance  will  be  only—  of  the  resistance  of  any  one  file, 
or  will  be  -rt  hence,  by  Ohm's  law,  such  a  battery  would 
give  as  its  current 

C  = 
= 


It  can  be  shown  mathematically  that,  for  a  given  battery  of  cells,  the  most 
effective  way  of  grouping  them  when  they  are  required  to  work  through  a 
given  external  resistance  R,  is  so  to  choose  m  and  n,  that  the  internal 
resistance  ('—  r)  shall  equal  the  external  resistance.  The  student  should 

verify  this  rule  by  taking  examples  and  working  them  out  for  different 
groupings  of  the  cells.  Although  this  arrangement  gives  the  strongest  current 
it  is  not  the  most  economical  ;  for  if  the  internal  and  external  resistances  be 
equal  to  one  another,  the  useful  work  in  the  outer  circuit  and  the  useless 
work  done  in  heating  the  cells  will  be  equal  also,  half  the  energy  being 
wasted.  The  greatest  economy  is  attained  when  the  external  resistance  is 
very  great  as  compared  with  the  internal  resistance  ;  only,  in  this  case,  the 
materials  of  the  battery  will  be  consumed  slowly,  and  the  current  will  not  be 
drawn  off  at  its  greatest  possible  strength. 


314  ELEMENTARY  LESSONS  ON       [CHAP.  vi. 

352.  Long  and  Short  Coil  Instruments. — The  student  will 
also  now  have  no  difficulty  in  perceiving  why  a  "long-coil" 
galvanometer,  or  a  "  long-coil "  electromagnet,  or  instrument  of 
any  kind  hi  which  the  conductor  is  a  long  thin  wire  of  high 
resistance,  must  not  be  employed  on  circuits  where  both  R  and 
r  are  already  small.     He  will  also  understand  why,  on  circuits 
of  great  length,  or  where  there  is  of  necessity  a  high  resistance 
and  a  battery  of  great  electromotive  force  is  employed,  "  short- 
coil  "  instruments  are  of  little  service,  for  though  they  add  little 
to  the  resistances  their  few  turns  of  wire  are  not  enough  with 
the  small  currents  that  circulate  in  high-resistance  circuits  ;  and 
why  "  long-coil "  instruments  are  here  appropriate  as  multiplying 
the  effects  of  the  currents  by  their  many  turns,  their  resistance, 
though  perhaps  large,  not  being  a  serious  addition  to  the  existing 
resistances  of  the  circuit.     A  galvanometer  with  a  "long-coil  " 
of  high  resistance,  if  placed  as  a  shunt  across  two  points  of  a 
circuit,  will  draw  therefrom  a  current  proportional  to  the  differ- 
ence of  potential  between  those  points.     Hence  such  an  instru- 
ment may  be  used  as  a  voltmeter  (Art.  360  d.) 

353.  Divided  Circuits. — If  a  circuit  divides,  -as  in 
Fig.  129,  into  two  branches  at  A,  uniting  together  again 

at  B,  the  -current  will  also 
be  divided,  part  flowing 
through  one  branch  part 
through  the  other.  The 
relative  strengths  of  cur- 
rent in  the  tuio  branches 
will  be  proportional  to 
their  conductivities,  i.e.. 

Fig   120 

inversely  proportional  to 

their  resistances.  Thus,  if  r  be  a  wire  of  2  ohms  re- 
sistance and  r1  3  ohms,  then  current  in  r:  current  in 
•>  =  /:r 

=  3:2, 

or,  -|  of  the  whole  current  will  flow  through  r,  and  -|  of 
the  whole  current  through  /. 

The  joint  resistance  of  the  divided  circuit  between  A 
and  B  will  be  less  than  the  resistance  of  either  branch 
singly,  because  the  current  has  now  choice  of  either  path. 
In  fact,  the  joint  conductivity  will  be  the  sum.  of  the  two 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  315 

separate  conductivities.     And  if  we  call  the  joint  resist 
ance  R.  it  follows  that 


_  -»  ±  4-  -  — 


r'  +  r 


R        r        r'  rr'    > 

whence    R   =    ~.^~j    or,    in    words,    the  joint 

resistance  of  a  divided  conductor  is  equal  to  the  product 
of  tJie  two  separate  resistances  divided  by  their  sum. 

Kirchhoft  has  given  the  following  important  laws,  both  cf 
them  deducible  from  Ohm's  law. 

(i. )  In  any  branching  network  of  wires  the  algebraic  sum  of 
the  currents  in  all  the  wires  that  meet  in  any  point  is 
zero. 

(ii. )  When  there  are  several  electromotive -forces  acting  at 
different  points  of  a  circuit,  the  total  electromotive -force 
round  the  circuit  is  equal  to  the  sum  of  the  resistances 
of  its  separate  parts  multiplied  each  into  the  strength  of 
the  current  that  flows  through  it. 

354.  Current  Sheets. — When  a  current  enters  a 
solid  conductor  it  no  longer  flows  in  one  line  but  spreads 
out  and  flows  through  the  mass  of  the  conductor.  "\\  hen 
a  current  is  led  into  a  thin  plate  of  conducting  matter  it 
spreads  out  into  a  "current  sheet  "and  flows  through 
the  plate  in  directions  that  depend  upon  the  form  of  the 
plate  and  the  position  of  the  pole  by  which  it  returns  to 
the  batter>\  Thus,  if  wires  from  the  two  poles  of  a 
battery  are  brought  into  contact  with  two  neighbouring 
points  A  and  B  in  the  middle  of  a  very  large  flat  sheet 
of  tinfoil,  the  current  flows  through  the  foil  not  in  one 
straight  line  from  A  to  B,  but  in  curving  "lines  of  flov\," 
which  start  out  in  all  directions  from  A,  and  curl  round  to 
meet  in  B,  in  curves  very  like  those  of  the  "  lines  offeree  " 
that  run  from  the  N.-pole  to  the  S.-pole  of  a  magnet 
(Fig.  50).  When  the  earth  is  used  as  a  return  wire  to 
conduct  the  telegraph  currents  (Fig.  160),  a  similar 
spreading  of  the  currents  into  current  bheets  occurs. 


316  ELEMENTARY  LESSONS  ON      [CHAP.  VL 


LESSON  XXX. — Electrical  Measurements. 

355.  The  practical  electrician  has  to  measure  electri- 
cal resistances,  electromotive -forces,  and  the  capacities 
of  condensers.      Each   of   these  several  quantities   is 
measured  by  comparison  with  ascertained  standards,  the 
particular  methods  of  comparison  varying,  however,  to 
meet  the  circumstances  of  the  case.     Only  a*  few  simple 
cases  can  be  here  explained. 

356.  Measurement  of  Resistance.  —  Resistance 
is  that  which  stops  the  flow  of  electricity.     Ohm's  law 
shows  us  that  the  strength  of  a  current  due  to  an  electro- 
motive force  falls  off  in  proportion  as  the  resistance  in 
the  circuit  increases. 

(a)  It  is  therefore  possible  to  compare  two  resistances 
with  one  another  by  finding  out  in  what  proportion  each 
of  them  will  cause  the  current  of  a  constant  battery  to 
fall  off.  Thus,  suppose  in  Fig.  128  we  have  a  standard 
battery  of  a  few  Daniell's  cells,  joined  up  in  circuit  with 
a  wire  of  an  unknown  resistance  R,  and  with  a  galvan- 
ometer, we  shall  obtain  a  current  of  a  certain  strength, 
as  indicated  by  the  galvanometer  needle  experiencing  a 
certain  deflection.  If  we  remove  the  wire  R,  and  sub- 
stitute in  its  place  in  the  circuit  wires  whose  resistances 
we  'know,  we  may,  by  trying,  find  one  which,  when  inter- 
posed  in  the  path  of  the  current,  gives  the  same  deflection 
on  the  galvanometer.  Hence  we  shall  know  that  this 
wire  and  the  one  we  called  R  offer  equal  resistance  to 
the  current.  Such  a  process  of  comparison,  which  we 
may  call  a  method  of  substitution  of  equivalent  resistances, 
was  further  developed  by  Wheatstone,  Jacobi,  and  others, 
when  they  proposed  to  employ  as  a  standard  resistance 
a  long  thin  wire  coiled  upon  a  wooden  cylinder,  so  that 
any  desired  length  of  the  standard  wire  might  be  thrown 
into  the  circuit  by  unwinding  the  proper  number  of  turns 
of  wire  off  the  cylinder,  or  by  making  contact  at  some 
point  at  any  desired  distance  from  the  end  of  the  wire. 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  317 

Such  an  instrument  was  known  as  a  Rheostat,  but  it  is 
now  superseded  by  the  resistance  coils  explained  below. 

(b)  The  method  explained   above  can  be   used  with 
any  galvanometer    of  sufficient  sensitiveness,  but  if  a 
tangent  galvanometer  is  available  the  process  may  be 
shortened  by  calculation.     Suppose  the  tangent  galvano- 
meter and  an  unknown  resistance  R  to  be  included  in 
the  circuit,  as  in  Fig.  128,  and  that  the  current  is  strong 
enough  to  produce  a  deflection  of  3  degrees :  Now  sub- 
stitute for  R  any  known  resistance  R',  which  will  alter  the 
deflection  to  d' ;  then  (provided  the  other  resistances  of 
the  circuit  be  negligibly  small)  it  is  clear  that  since  the 
strengths  of  the  currents  are  proportional  to  tan  d  and 
tan  d'  respectively,  the  resistance  R  can  be  calculated  by 
the  inverse  proportion. 

tan  8:  tan  $  &  R'  :  R. 

(c)  With  a  differential  galvanometer  (Art.  203),  and  a 
set  of  standard  resistance  coils,  it  is  easy  to  measure  the 
resistance  of  a  conductor.  -  Let  the  circuit  divide  into  two 
branches,  so  that  part  of  the  current  flows  through  the 
unknown  resistance  and  round  one  set  of  coils  of  the 
galvanometer,  the  other  part  of  the  current  being  made 
to  flow  through  the  known  resistances  and  then  round 
the  other  set  of  coils  in  the  opposing  direction.     When 
we  have  succeeded  in  matching  the  unknown  resistance 
by  one  equal  to  it  from  amongst  the  known  resistances, 
the  currents  in  the  two  branches  will  be  equal,  and  the 
needle    of  the   differential   galvanometer  will    show   no 
deflection.    With  an  accurate  instrument  this  null  method 
is  very  reliable. 

(d)  The  best  of  all  the  ways  of  measuring  resistances 
is,  however,  with  a  set  of  standard  resistance  coils  and 
the  important  instrument  known  as  Wheatstone's  Bridge, 
described  below  in  Art.  358. 

(e)  To  measure  very  high  resistances  the  plan  may  be 
adopted  of  charging  a  condenser  from  a  standard  battery 
for  a  definite  period   through  the  resistance,  and   then 


3«8  ELEMENTARY  LESSONS  ON       FCHAP.  vi. 

ascertaining  the  accumulated  charge  by  discharging  it 
through  a  ballistic  galvanometer  (Art.  204). 

357.  Fall  of  Potential  along  a  Wire.  —  To  understand  the 
principle  of  Wheatstone's  Bridge  we  must  explain  a  preliminary 
point.  If  the  electric  potential  of  different  points  of  a  circuit 
be  examined  by  means  of  an  electrometer,  as  explained  in  Art. 
263,  it  is  found  to  decrease  all  the  way  round  the  circuit  from 
the  +  pole  of  the  battery,  where  it  is  highest,  down  to  -  pole, 
where  it  is  lowest'.  If  the  circuit  consist  of  one  wire  of  uniform 
thickness,  which  offers,  consequently,  a  uniform  resistance  to 
the  current,  it  is  found  that  the  potential  falls  uniformly;  if 
however,  part  of  the  circuit  resists  more  than  another,  it  is 
found  that  the  potential  falls  most  rapidly  along  the  conductor 
of  greatest  resistance.  But  in  every  case  the  fall  of  potential 
between  any  two  points  is  proportional  to  the  resistance  between 
those  two  points  ;  and  we  know,  for  example,  that  when  we 
have  gone  round  the  circuit  to  a  point  where  the  potential  has 
fallen  through  half  its  value,  the  current  has  at  that  point  gone 
through  half  the  resistances.  The  difference  of  potential  e  be- 
tween the  poles  of  a  battery  (of  electromotive-force  E  and 
internal  resistance  r)  in  a  circuit  of  which  the  1  otal  resistance  is 
R  +  r,  may  be  written  in  the  following  ways  as  : 


358.  Wheatstone's  Bridge.  —  This  instrument, 
invented  by  Christie,  and  applied  by  Wheatstone  to 
measure  resistances,  consists  of  a  system  of  conductors 
shown  in  diagram  in  Fig.  130.  The  circuit  of  a  constant 
battery  is  made  to  branch  at  P  into  two  parts,  which 
re-unite  at  Q,  so  that  part  of  the  current  flows  through 
the  point  M,  the  other  part  through  the  point  N.  The 
four  conductors  D,  C,  B,  A,  are  spoken  of  as  the  "  arms  " 
of  the  "  balance  "  or  "  bridge  ;"  it  is  by  the  proportion 
subsisting  between  their  resistances  that  the  resistance 
of  one  of  them  can  be  calculated  when  the  resistances  cf 
the  other  three  are  known.  When  the  current  which 
starts  from  C  at  the  batter-/  arrives  at  P,  the  potential 
will  have  fallen  to  a  certain  value.  The  potential  of  the 
current  in  the  upper  branch  falls  again  to  M,  and 
j.  continues  to  fall  to  Q,  The  potential  of  the  lower 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM. 


branch  falls  to  N,  and  again  falls  till  it  reaches  the  value 
at  Q.      Now  if  N  'be  the  same  proportionate  distance 


130. 


along  the  resistances  between  P  and  Q,  as  M  is  along 
the  resistances  of  the  upper  line  between  P  and  Q,  the 
potential  will  have  fallen  at  N  to  the  same  value  as  it 
has  fallen  to  at  M  ;  or,  in  other  words,  if  the  ratio  of  the 
resistance  C  to  the  resistance  D  be  equal  to  the  ratio 
between  the  resistance  A  and  the  resistance  B,  then  M 
and  N  will  be  at  equal  potentials.  To  find  out  whether 
they  are  at  equal  potentials  a  sensitive  galvanometer  is 
placed  in  a  branch  wire  between  M  and  N  ;  it  will  show 
no  deflexion  when  M  and  N  are  at  equal  potentials  ;  or 
when  the  four  resistances  of  the  arms  "  balance  "  one 
another  by  being  in  proportion,  thus  :  — 

A:C::B:D. 

If,  then,  we  know  what  A,  B,  and  C  are,  we  can  calculate 
D,  which  will  be  TJ  v  r- 

D=   TT 

EXAMPLE.—  Thus  if  A  and  C  are  (as  in  Fig.  133)  10  ohms 
and  loo  ohms  respectively,  and  B  be  15  ohms,  D  will 
be  15  x  ioo  H-  10  =  150  ohms. 


320  ELEMENTARY  I.Ef.SONS  ON       [CHAP.  vi. 

359.  Resistance  Coils.— Wires  of  standard  resist- 
ance are  now  sold  by  instrument  makers  under  the  name 
of  Resistance  Coils.  They  consist  of  coils  of  german- 
silver  (see  Art.  349)  (or  sometimes  silver-iridium  alloy), 
wound  with  great  care,  and  adjusted  to  such  a  length  as 
to  have  resistances  of  a  definite  number  otohins.  In  order 

to    avoid    self-induction, 
and  the  consequent  sparks 
(see    Art.    404)    at    the 
J    opening  or  closing  of  the 
circuit,    they   are    wound 
in    the    peculiar   manner 
indicated    in    Fig.    131,, 
each  wire   (covered  with 
Fig.  I3I<  silk  or  paraffined -cotton) 

being    doubled    on    itself 

before  being  coiled  up.  Each  end  of  a  coil  is  soldered 
to  a  solid  brass  piece,  as  coil  i  to  A  and  B,  coil  2  to 
B  and  C  ;  the  brass  pieces  being  themselves  fixed  to  a 
block  of  ebonite  (forming  the  top  of  the  "resistance 
box "),  with  sufficient  room  between  them  to  admit  of 
the  insertion  of  stout  well-fitting  plugs  of  brass.  Fig. 
132  shows  a  complete  resistance -box,  as  fitted  up  for 


Fig.  132. 


electrical  testing,  with  the  plugs   in   their  places.      So 
long  as  the  plugs  remain  in,  the  current  flows  through. 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM. 


321 


the  selid  brass  pieces  and  plugs  without  encountering 
any  serious  resistance ;  but  when  any  plug  is  removed, 
the  current  can  only  pass  from  the  one  brass  piece  to 
the  other  by  traversing  the  coil  thus  thrown  into  circuit. 
The  series  of  coils  chosen  is  usually  of  the  following 
numbers  of  ohms'  resistance — i,  2,  2,  5  ;  10,  20,  20, 

50;  100,  200,  200,  500  ; up  to  10,000  ohms. 

By  pulling  out  one  plug  any  one  of  these  can  be  thrown 
into  the  circuit,  and  any  desired  whole  number,  up  to 
20,000,  can  be  made  up  by  pulling  out  more  plugs  ;  thus 
a  resistance  of  263  ohms  will  be  made  up  as  200  -f  50 
+  10  +  2  +  i. 

It  is  usual  to  construct  Wheatstone's  bridges  with  some 
resistance  coils  in  the  arms  A  and  C,  as  well  as  with  a 
complete  set  in  the  arm  B.  The  advantage  of  this 

1C. 


N 


Fig.  133. 


arrangement  is  that  by  adjusting  A  and  C  we  determine 
the  proportionality  between  B  and  D,  and  can,  in  certain 
cases,  measure  to  fractions  of  an  ohm.  Fig.  133  shows 
P  more  complete  scheme,  in  which  resistances  of  10,  100, 
.and  1000  ohms  are  included  in  the  arms  A  and  C, 


322  ELEMENTARY  LESSONS  ON       [CHAP.  vi. 

EXAMPLE. — Suppose  we  had  a  wire,  wnose  resistance  we 

knew  to  be  between  46  and  47  ohms,  and  wished  to 

measure  the  fraction  of  an  ohtn,  we  should  insert  it  at  D, 

and  make  A  100  ohms  and  C  10  ohms  ;  in  that  case  D 

would  be  balanced  by  a  resistance  in  B  10  times  as  great 

as  the  wire  D.     If,  on  trial,  this  be  found  to  be  464  okms 

we  know  that  D  =  464  x  10  -f-  IOQ  =  46-4  ohins. 

In  practice  the  bridge  is  seldom  or  never  made  in  the 

lozenge -shape  of  the  diagrams.     The  resistance -box  of 

Fig.  132  is,  in  itself,  a  complete  "bridge,"  the  appropriate 

connections  being  made  by  screws  at  various  points.     In 

using  the  bridge  the  battery  circuit  should  always  be 

completed  by  depressing  the   key   Kx  before    the   key 

K3  of  the  galvanometer  circuit  is  depressed,   in    order 

to  avoid  the  sudden  violent  "  throw  "  of  the  galvanometer 

needle,  which  occurs  on  closing  circuit  in  consequence  of 

self-induction  (Art.  404). 

36O.  Measurement  of  Electromotive-Force. — 
There  being  no  easy  absolute  method  of  measuring 
electromotive-forces,  they  are  usually  measured  relatively, 
by  comparison  with  the  electromotive-force  of  a  standard 
cell,  such  as  that  of  Daniell  (Art.  170),  or  better  still 
that  of  Latimer  Clark  (Art.  177).  The  methods  of 
comparison  are  various  ;  only  four  can  here  be  men- 
tioned. 

(a)  Call  E  the  electromotive-force  of  the  battery  to  be 
measured,  and  E'  that  of  a  standard  battery.  •  Join  E 
with  a  galvanometer,  and  let  it  produce  a  deflection  of 
$1  degrees  through  the  resistances  of  the  circuit ;  then 
add  enough  resistance  r  to  bring  down  the  deflection  to 
8a  degrees — say  10  degrees  less  than  before.  Now 
substitute  the  standard  battery  in  the  circuit  and  adjust 
the  resistances  till  the  deflection  is  5i  as  before,  and  then 
add  enough  resistance  r1^  to  bring  down  the  deflection 
to  Ss.  Then 

r1  :  r  =  E'  :  E, 

F:nce  the  resistances  that  will  reduce  the  strength  of  the 
current  equally  will  be  proportional  to  the  electromotive- 
forces 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  323 

(l>)  If  the  poles  of  a  standard  battery  are  joined  by  a  long 
thin  wire,  the  potential  will  fall  uniformly  from  the  +  to 
the  —  pole.  Hence,  by  making  contacts  at  one  pole 
and  at  a  point  any  desired  distance  along  the  wire,  any 
desired  proportional  part  of  the  whole  electromotive-force 
can  be  taken.  This  proportional  part  may  be  balanced 
against  the  electromotive-force  of  any  other  battery,  or 
used  to  compare  the  difference  between  the  electromotive- 
forces  of  two  different  cells. 

(f)  The  electromotive-force  of  a  battery  may  be  measured 
directly  as  a  difference  of  potentials  by  a  quadrant  electro- 
meter. In  this  case  the  circuit  is  never  closed,  and  no 
current  flows. 

(d)  If  a  galvanometer  be  constructed  so  that  the  resistance 
of  its  coils  is  several  thousand  ohms,  in  comparison  with 
which  the  internal  resistance  of  a  battery  or  dynamo 
machine  is  insignificant,  such  a  galvanometer  will  serve 
to  measure  electromotive-forces  ;  for,  by  Ohm's  law,  the 
strength  of  current  which  such  a  battery  or  dynamo  can 
send  through  it  will  depend  only  on  the  electromotive- 
force  between  the  ends  of  the  coil.  Such  a  galvanometer, 
suitably  graduated,  is  sometimes  called  a  "  Vclt-metern 
or  "  Potential  galvanometer  "  It  can  be  used  to  determine 
the  difference  of  potential  between  any  two  points  of  a 
circuit  by  connecting  its  terminals  as  a  shunt  to  the 
circuit  between  these  two  points. 

361.  Measurement  of  Internal  Resistance  of 
Battery. — This  may  fee  done  in  three  ways. 

(a)  Note  by  a  tangent  galvanometer  the  strength  of  the 
current,  first,  when  the  resistance  of  the  external  circuit 
is  small ;  and  secondly,  when  a  larger  known  external 
resistance  is  introduced.  From  this  the  proportion 
between  the  internal  resistance  and  the  introduced  ex- 
ternal resistance  can  be  calculated. 

(3)  (Method  of  Opposition). — Take  two  similar  cells  and 
join  them  in  opposition  to  one  another,  so  that  they  send 
no  current  of  their  own.  Then  measure  their  united 
resistance  just  as  the  resistance  of  a  wire  is  measured. 
The  resistance  of  one  cell  will  be  half  that  of  the  two. 

(c)  (MancSs  Method). — Place  the  cell  itself  in  one  arm  of 
the  Wheatstone's  bridge,  and  put  a  key  where  the  battery 
usually  is,  adjust  the  resistances  till  the  permanent  galvano- 


324  ELEMENTARY  LESSONS  ON      [CHAP.  VI, 

meter  deflection  is  the  same  whether  the  key  be  depressed 
or  not.  When  this  condition  of  things  is  attained  the 
battery  resistance  is  balanced  by  those  of  the  other  three 
arms.  (ATot  a  reliable  method.) 

362.  Measurement    of  Capacity    of   a    Con- 
denser.— The  capacity  of  a  condenser  may  be  measured 
by  comparing  it  with  the  capacity  of  a  standard  con- 
denser— such  as  the  -^  microfarad  condenser  shown  in 
Fig.  1 06, — in  one  of  the  following  ways  : — 

(a)  Charge  the  condenser  of  unknown  capacity  to  a 
certain  potential ;  then  make  it  share  its  charge  with  the 
condenser  of  known  capacity,  and  measure  the  potential 
to  which  the  charge  sinks  :  then  calculate  the  original 
capacity,  which  will  bear  the  same  ratio  to  the  joint 
capacity  of  the  two  as  the  final  potential  bears  to  the 
original  potential. 

(&)  Charge  each  condenser  to  equal  differences  of 
potential,  and  then  discharge  each  successively  through 
a  ballistic  galvanometer  (Art.  204),  when  the  sine  of  half 
the  angle  of  the  first  swing  of  the  needle  will  be  propor- 
tional in  each  case  to  the  charge,  and  therefore  to  the 
capacity. 

(c)  Charge  the  two   condensers  simultaneously  from 
one  pole  of  the  same  battery,  interposing  high  resistances 
in  each  branch,  and  adjusted  so  that  the  potential  rises 
at  an  equal  rate  in  both;  then  the  capacities  are  inversely 
proportional  to  the  resistances  through  which  they  are 
respectively  being  charged. 

(d)  Another  method,  requiring  no  standard  condenser. 
is  as  follows  : — Allow  the  condenser,  uhose  capacity  is  to 
be  measured,  to  discharge  itself  slowly  through  a  wire  of 
very  high  resistance.     The  time  taken  by  the  potential 
to  fall  to  any  given  fraction  of  its  ori/inal  value  is  pro- 
portional to  the  resistance,  to  the  capacity,  and  to  the 
logarithm  of  the  given  fraction. 

363.  Kesistance   Expressed   as   a   Velocity.  —  It  Mill  be 
seen,  on  reference  to  the  table  of  "  Dimensions "  of  electro- 
magnetic units  (Art.  324),  that  the  dimensions  of  resistance  arc 


CHAP,  vi.]    ELECTRICITY  AND  MAGNETISM.  325 

given  as  LT~l,  which  are  the  same  dimensions  (see  Art.  258)  as 
those  of  a  velocity.  Every  resistance  is  capable  of  being 
expressed  as  a  velocity.  The  following  considerations  may 
assist  the  student  in  forming  a  physical  conception  of  this  : — 
Suppose  we  have  a  circuit  composed  of  two  horizontal  rails 


[  1 

I 

*D                                              Cj 
*&                                             «( 

C3   1 

j 

// 

FTP 

\f   \f^Sf    > 

D  "A.  T 

Fig.  134. 

(Fig.  134),  CS  and  DT,  i  centim.  apart,  joined  at  CD,  and 
completed  by  means  of  a  sliding  piece  AB.  Let  this  variable 
circuit  be  placed  in  a  uniform  magnetic  field  of  unit  intensity, 
the  lines  of  force  being  directed  vertically  downwards  through 
the  circuit.  If,  now,  the  slider  be  moved  along  towafds  ST 
with  a  velocity  of  n  centimetres  per  second,  the  number  of 
additional  lines  of  force  embraced  by  the  circuit  will  increase  at 
the  rate  n  per  second  ;  or,  in  other  words,  there  will  be  an 
induced  electromotive  -  force  (Art.  394)  impressed  upon  th3 
circuit,  which  will  cause  a  current  to  flow  through  the  slider 
from  A  to  B.  Let  the  rails  have  no  resistance,  then  the 
strength  of  the  current  will  depend  on  the  resistance  of  AB. 
Now  let  AB  move  at  such  a  rate  that  the  current  shall  be  of 
unit  strength.  If  its  resistance  be  one  "absolute"  (electro- 
magnetic) unit  it  need  only  move  at  the  rate  of  I  centim.  per 
second.  If  its  resistance  be  greater  it  must  move  with  a  pro- 
portionately greater  velocity ;  the  velocity  at  which  it  must 
move  to  keep  up  a  current  of  unit  strength  being  numerically 
equal  to  its  resistance.  77; e  resistance  known  as  "  one  ohm  "  is 
intended  to  be  io9  absolute  electromagnetic  units,  and  therefore  is 
represented  by  a  velocity  <7/"lo9  centimetres,  or  ten  million  metres 
(one  earth-quadrant)  per  second. 

&A.  Evaluation  of  the  Ohm. — The  value  of  the  ohm  in  absolute  measure 
was  determined  by  a  Committee  of  the  British  Association  in  London  in  1863. 
It  being  impracticable  to  give  to  a  horizontal  sliding-piece  so  high  a  velocity 
as  was  necessitated,  the  velocity  which  corresponded  to  the  resistance  of  a 
wire  was  measured  in  the  following  'way: — A  ring  of  wire  (of  many  turns), 
pivoted  about  a  vertical  axis,  as  in  Fig.  135,  was  made  to  rotate  very  rapidly 
and  uniformly.  Such  a  ring  in  rotating  cuts  the  lines  of  force  of  the  earth's 
magnetism.  The  northern  half  of  the  ring,  in  moving  from  west  toward  east. 


3*6 


ELEMENTARY  LESSONS  ON 


[CHAP  vi. 


will  have  (sec  Rule  Art.  395)  an  upward  current  induced  in  it,  while  the 
southern  .half,  in  crossing  from  east  toward  west,  will  have  a  downward 

current  induced  in  it.  Hence  the 
rotating  ring  will,  as  it  spins,  act 
as  its  own  galvanometer  if  a  small 
magnet  be  hung  at  its  middle  ;  the 
magnetic  effect  due  to  the  rotating 
coil  being  proportional  directly  to 
-N 


S — 


Fig.  135- 


the  horizontal  component  of  the 
earth's  magnetism,  to  the  velocity 
of  rotation,  and  to  the  number  of 
turns  of  wire  in  the  coil,  and  in- 
versely proportional  to  the  resist- 
ance of  the  wire  of  the  coils.  Hence, 
all  the  other  data  being  known,  the 
resistance  can  be  calculated  and 
measured  as  a  •velocity.  The 


existing  ohnts  or  B.A.  units  were  constructed  by  comparison  with  this 
totaling  coil ;  but  there  being  some  doubt  as  to  whether  the  B.  A.  unit  really 
represented  lo9  centirns.  per  second,  a  redeterminatiou  of  the  ohm  was 
suggested  in  1880  by  the  British  Association  Committee. 

364  (bis).  The  Legal  Ohm— At  the  International  Congress  of  Electricians 
in  Paris  1881  the  project  for  a  redetermination  of  the  ohm  was  endorsed,  and 
it  was  also  agreed  that  the  practical  standard?  should  no  longer  be  con- 
structed in  German  silver  wire,  but  that  they  should  be  made  upon  the  plan 
originally  suggested  by  Siemens,  Ly  defining  the  practical  ohm  as  the  resist- 
ance of  a  column  of  pure  mercury  of  a  certain  length,  and  of  one  millimetre 
of  cross-section.  The  original  "  Siemens'  unit "  was  a  column  of  mercury 
one  metre  in  length,  and  one  square  millimetre  in  section,  and  was  rather 
less  than  an  ohm  (o'g^s  B.A.  unit).  Acting  on  measurements  made  by  the 
1-est  physicists  of  Europe,  tl»e  Paris  Congress  of  1884  decided  that  the 
mercury  column  representing  fhe  legal  ohm  shall  be  106  centimetres  in 
length.  [Lord  Rayleigh's  deteiminatien  gave  106*21  centimetres  of  mercury, 
as  representing  the  true  theoretical  olim  (=  10$  absolute  units).]  Our  old 
B.A.  ohm  is  only  o'gSS;  of  the  new  legal  ohm  ;  and  our  old  volt  is  0-9887  of 
the  legal  volt. 


NOTE  ON  THE  RATIO  OF  THE  ELECTROSTATIC  TO  THE 
ELECTROMAGNETIC  UNITS. 

365.  If  the  student  will  compare  the  Table  of  Dimensions  of  Electrostatic 
Units  of  Ait.  258  with  that  of  the  Dimensions  of  Electromagnetic.  Units  of 
Art.  324,  he  will  observe  that  the  dimensions  assigned  to  similar  units  aro 
different  ip.  the  two  systems.  Thus,  the  dimensions  of  "Quantity"  in 
electrostatic  measure  are  M*  L*  T~  ,  and  in  electromagnetic  measure  are 
M*  L-'  Dividing  the  former  by  the  latter  we  get  LT"1'  a  quantity  which 


CHAP.  vi.J    ELECTRICITY  AND  MAGNETISM. 


327 


we  at  once  see  is  of  the  nature  of  a  velocity.  This  velocity  occurs  in  every 
case  in  the  ratio  of  the  electrostatic  to  the  electromagnetic  measure  of  every 
unit.  It  is  a  definite  concrete  velocity,  and  represents  that  velocity  at  which 
two  electrified  particles  must  travel  along  side  by  side  in  order  that  their 
mutual  electromagnetic  attraction  (considered  as  equivalent  in  moving  to 
two  parallel  currents)  shall  just  equal  their  mutual  electrostatic  repulsion, 
tee  Art  337.  This  velocity,  "v,"  which  is  of  enormous  importance  in  the 
tlectrontagnetic  theory  of  light  (Art.  390),  has  been  measured  in  several  way». 


UNIT. 

ELECTROSTATIC. 

ELECTROMAGNETIC. 

RATIO 

Quantity 

M*  L*  T-1 

i       i 

LT-1     =  v 

Potential     . 

M*  L*  T-1 

M*  L*  T-» 

L-1  T  =  - 

Capacity 

L 

L_i  Ta 

L2  "p—  3  _  yjl 

Resistance  . 

L-1  T 

LT-1 

L-2  72  _  1_ 

(a)  Weber  and  Kohlrausch  measured  the  electrostatic  unit  of  quantify 
and  compared  it  with  the  electromagnetic  unit  of  quantity,  and  found  the  ratio 
v  to  be  =  3*1074  X  ic10  centims.  per  second.* 

(£)  Sir  W.  Thomson  compared  the  two  units  of  potential  and  found 

v  =  2-825     X  io*«, 

and  later,  =  2'93       X  lo1'. 

(c)  Professor  Clerk  Maxwell  balanced  a  force  of  electrostatic  attraction 
against  one  of  electromagnetic  repulsion,  and  found 

v  =  a '88       X  i<A*. 

(ft)  Professors  Ayrton  and  Perry  measured  the  capacity  of  a  condenser 
electromagnetically  by  discharging  it  into  a  ballistic  galvanometer,  and 
electrostatically  by  calculations  from  its  size,  and  found 

v  =  3-980     X  ic10. 

(e)  Professor  Joseph  J.  Thomson  compared  the  capacity  of  a  condenser 
as  measured  electrostatically  by  calculation  and  as  measured  electromag. 
netically  on  a  Wheatstone's  bridge,  and  deduced 

v  =  2-963     X  io*0. 

TJie  velocity  of  light  is  believed  to  be  =  2 '99  92  x  10*' ; 

or,  according  to  G.  Forbes's  latest  determination, 
the  velocity  of  r«/ light  is  3*9826  X  xo19. 

Assuming  as  a  mean  value  3  X 10™,  and  comparing  with  Arts.  257  and  323, 
we  get : — 

i  coulomb  =  3  X  io9      electrostatic  (C.G.S.)  units  of  quantity  ; 
i  volt         =  Jx  io-*    electrostatic  (C.G.S.)  units  of  potential ; 
i  farad     =  9  X 10^    electrostatic  (C.  G.  S.)  units  of  capacity ; 
i  chut         =  JXio-J1  electrostatic  (C.G.S.)  units  of  resistance. 


ELEMENTARY  LESSONS  ON      [CHAP.  vn 


CHAPTER    VII. 

HEAT,  LIGHT,  AND  WORK,  FROM  ELECTRIC  CURRENTS. 

LESSON  XXXI. — Heating  Effects  of  Currents. 

366.  Heat  and  Resistance. — A  current  may  do 
work  of  various  kinds,  chemical,  magnetic,  mechanical, 
and  tlieiinal.  In  every  case  where  a  current  does  work 
that  work  is  done  by  the  expenditure  of  part  of  the  energy 
of  the  current.  We  have  seen  that,  by  the  law  of  Ohm, 
the  current  produced  by  a  given  battery  is  diminished  in 
stiength  by  anything  that  increases  the  external  resistance. 
But  the  strength  of  the  current  may  be  diminished,  in 
certain  cases,  by  another  cause,  namely,  the  setting  up 
of  an  opposing  electromotive  force  at  some  point  of  the 
circuit.  Thus,  in  passing  a  current  through  a  voltameter 
(Art.  214)  there  is  a  diminution  due  to  the  resistance  of 
the  ^  oltameter  itself,  and  a  further  diminution  due  to  the 
opposing  electromotive -force  (commonly  referred  to  as 
"  polarisation ")  which  is  generated  while  the  chemical 
work  is  being  done.  So,  again,  when  a  current  is  used  to 
drive  an  electromagnetic  motor  (Art.  375),  the  rotation 
of  the  motor  will  itself  generate  a  back- current,  which 
-will  diminish  the  strength  of  the  current.  Whatever 
current  is,  however,  not  expended  in  this  way  in  external 
work,  is  frittered  down  into  heat,  either  in  the  battery  or 
in  some  part  of  the  circuit,  or  in  both.  Suppose  a 
quantity  of  electricity  to  be  set  flowing  round  a  closed 
circuit.  If  there  were  no  resistance  to  stop  it  it  would 


CHAT,  vii.]     ELECTRICITY  AND  MAGNETISM. 


329 


circulate  for  ever ;  just  as  a  waggon  set  rolling  along  a 
circular  railway  should  go  round  for  ever  if  it  were  not 
stopped  by  friction.  "When  matter  in  motion  is  stopped 
by  fiiction  the  energy  of  its  motion  is  frittered  down  by 
the  friction  into  heat.  When  electricity  in  motion  is 
stopped  by  resistance  the  energy  of  its  flow  is  frittered 
do\\n  by  the  resistance  into  heat.  Heat,  in  fact,  appears 
wherever  the  circuit  offers  a  resistance  to  the  current. 
If  the  terminals  of  a  battery  be  joined  by  a  short  thick 
wire  of  small  resistance,  most  of  the  heat  will  be  de- 
veloped in  the  batter)' ;  whereas,  if  a  thin  wire  of  con- 
siderable resistance  be  interposed  in  the  outer  circuit,  it 
will  grow  hot,  while  the  battery  itself  will  remain  com- 
paratively cool. 

367.  Laws  of  Development  of  Heat :  Joule's 
Law. — To  investigate  the 
development  of  heat  by  a 
current,  Joule  and  Lenz  used 
instruments  on  the  prin- 
ciple of  Fig.  136,  in  which 
a  thin  wire  joined  to  two 
stout  conductors  is  enclosed 
within  a  glass  vessel  con- 
taining alcohol,  into  which 
also  a  thermometer  dips, 
The  resistance  of  the  wire 
being  known,  its  relation  to 
the  other  resistances  can 
be  calculated.  Joule  found 
that  the  number  of  units  of  heat  developed  in  a  con- 
ductor is  proportional — 

(i.)  to  its  resistance  ; 

(ii.)  to  the  square  of  the  strength  of  the  current ; 
and 

(in.)  to  the  time  that  the  current  lasts. 
The  equation  expressing  these  relations  is  known  as 
Joule's  Law,  and  is — 

Z 


Fig.  136. 


330  ELEMENTARY  LESSONS  ON     [CHAP,  vii. 

H  =  C2Rt   x   0-24 

where  C  is  the  current  in  amperes,  R  the  resistance  in 
ohms,  /  the  time  in  seconds,  and  H  the  heat  in  the  usual 
unit  of  heat-quantities,  viz.  the  amount  of  heat  that  will 
raise  I  gramme  of  water  through  i°C  of  temperature 
(Art.  255). 

Joule's  law  may  be  arrived  at  by  the  following  calculation. 
The  work  W  done  by  a  current  in  moving  Q  units  of  electricity 
through  a  difference  of  potential  V,  -  Vj  is  — 

W  =  Q(V8-VO; 

and  since  Q  =  Ct,  and  V,  -  Vl  =  E,  and  W  =  JH,  (where  J  is 
Joule's  equivalent  =  4  '2  x  to7,  and  H  the  heat  in  water-gramme- 
centigrade  degree  units),  we  have  — 

JH  =±  CtE  (and  E  =  CR). 

=  C2Rt 


,  TT 

whence       H  = 

But  as  C  and  R  are  here  in  "  absolute  "  units,  they  must  be 
multiplied  by  10  —  2  x  io9  =  io7,  to  reduce  to  the  ordinary  case 
of  amperes  and  ohms  ;  whence  — 

H  =  C2Rt  -T-  4'2 
=  C2Rt  x  0-24. 

This  is  equivalent  to  the  statement  that  a  current  of 
one  ampere  flowing  through  a  resistance  of  one  ohm 
developes  therein  0*24  heat  -units  per  second. 

Dr.  Siemens  proposes  to  call  this  quantity  of  heat  (or  its 
mechanical  equivalent  in  work)  by  the  name  of  one  joule.  If 
this  suggestion  be  adopted,  the  electric  unit  of  heat,  the  joule, 
will  be  only  0-24  of  an  ordinary  heat-unit.  or  calorie  (Art.  255), 
and  i  calorie  will  be  equal  to  4  '2  joules. 

The  second  of  the  above  laws,  that  the  'heat  is,  catens  paribus,  propor- 
tional to  the  square  of  the  strength  of  the  current,  often  puzzles  young 
students,  who  expect  the  heat  to  be  proportional  to  the  current  simply. 
Such  may  remember  that  the  consumption  of  *zinc  is,  ceeteris  paribust  also 
proportional  to  the  square  of  the  current  ;  for,  suppose  that  in  working 
through  a  high  resistance  (so  as  to  get  all  the  heat  developed  outside  the 
battery)  we  double  the  current  by  doubling  the  number  of  battery  cells,  there 
will  be  twice  as  much  zinc  consumed  as  before  in  each  cell,  and  as  there  are 
twice  as  many  cells  as  at  first  the  consumption  of  zinc  is  four  times  as  great 
as  before. 

363.  Fa  vre  s  Experiments.  —  'Favre  made  a  series  of  most 
important  experiments  on  the  relation  of  the  energy  of  a  current 


CHAP,  vii.]    ELECTRICITY  AND  MAGNETISM.         331 

to  the  heat  it  developes.     He  ascertained  that  the  number  of 
heat-units  evolved  when  33  grammes  (I  equivalent)  of  zinc  are 
dissolved  in  dilute  sulphuric  acid  (from  which  it  causes  hydrogen 
to  be  given  off)  to  be  18,682.     This  figure  was  arrived  at  by 
conducting  the  operation  in  a  vessel  placed  in  a  cavity  of  his 
calorimeter,  an  instrument  resembling  a  gigantic  thermometer 
filled  with  mercury,  the  expansion  of  which  was  proportional  to 
the  heat  imparted  to  it.     When  a  Smee's  cell  was  introduced 
into  the  same  instrument,  the  solution  of  the  same  amount  of 
zinc  was  observed  to  be  accompanied  by  the  evolution  of  18,674 
units  of  heat  (i.e.  an  amount  almost  identical  with  that  observed 
before),  and  this  amount  was  the  same  whether  the  evolution 
took  place  in  the  battery-cell  when  the  circuit  was  closed  with  a 
short  thick  wire,  or  whether  it  took  place  in  a  long  thin  wire 
placed  in  the  external  circuit.     He  then  arranged  5  Smee's  cells 
in  series,  in  cavities  of  the  calorimeter,  and  sent  their  current 
round  a  small  electromagnetic  engine.     The  amount  of  heat 
evolved  during  the  solution  of  33  grammes  of  zinc  was  then 
observed  in  three  cases  ;  (i.)  when  the  engine  was  at  rest ;  (ii.) 
when  the  engine  was  running  round  and  doing  no  work  beyond 
overcoming  the  friction  of  its  pivots  ;  (iii.)  when  the  engine  was 
employed  in  doing  13,124,000  gramme-centimetres  (=  12,874 
x  io6  ergs)  of  work,  by  raising  a  'weight  by  a  cord  running  over 
a  pulley.     The  amounts  of  heat  evolved  hi  the  circuit  in  the 
three  cases  were  respectively,  18,667,  18.657,  and  18,374  units. 
In  the  last  case  the  work  done  accounts  for  the  diminution  in 
the  heat  frittered  down  in  the  circuit.     If  we  add  the  heat- 
equivalent  of  the  work  done  to  the  heat  evolved  hi  the  latter 
case,  we  ought  to  get  the  same  value  as  before.     Dividing  the 
12,874  x  io6  ergs  of  work  by  Joule's  equivalent,  expressed  in 
"absolute"  measure  (42  x  io6),  we  get  as  the  heat-equivalent  of 
ihe  work  done  306  heat  units.     Now  18,374  +  306  =  18,680, 
a  quantity  which   is   almost   identical    with   that  of  the  first 
observation,  and  quite  within  the  limits  of  unavoidable  experi- 
mental error. 

369.  Rise  of  Temperature.  —  The  elevation  of 
temperature  in  a  resisting  wire  depends  on  the  nature  of 
the  resistance.  A  very  short  length  of  a  very  thin  wire  may 
resist  just  as  much  as  a  long  length  of  stout  wire.  Each 
will  cause  the  same  number  of  units  of  heat  to  be  evolved, 
but  in  the  former  case,  as  the  heat  is  spent  in  warming  a 


3?2  ELEMENTARY  LESSONS  ON     [CHAP.  vii. 

short  thin  wire  of  small  mass,  it  will  get  very  hot,  whereas 
in  the  latter  case  it  will  perhaps  only  warm  to  an  imper- 
ceptible degree  the  mass  of  the  long  thick  wire.  If  the 
wire  weigh  «/  grammes,  and  have  a  specific  capacity  foi 
heat,  s,  then  H  =  sw0,  where  6  is  the  rise  of  tempera- 
ture in  degrees  (Centigrade).  Hence 

a  C2R/  • 

6  =  0-24  x • 

sw 

Since  the  resistance  of  metals  increases  as  they  rise  in 
temperature,  a  thin  wire  heated  by  the  current  will  resist 
more,  and  grow  hotter  and  hotter  until  its  rate  of  loss  of 
heat  by  conduction  and  radiation  into  the  surrounding 
air  equals  the  rate  at  which  heat  is  supplied  by  the 
current. 

The  following  pretty  experiment  illustrates  the  laws  of 
heating.  The  current  from  a  few  cells  is  sent  through  a 
chain  made  of  alternate  links  of  silver  and  platinum 
wires.  The  platinum  links  glow  red-hot  whils  the  silver 
links  remain  comparatively  cool.  The  explanation  is 
that  the  specific  resistance  of  platinum  is  about  six  times' 
that  of  silver,  and  its  capacity  for  heat  about  half  as 
great ;  hence  the  Vise  of  temperature  in  wires  of  equal 
thickness  traversed  by  the  same  current  is  roughly  twelve 
times  as  great  for  platinum  as  for  silver. 

,  Thin  wires  heat  much  more  rapidly  than  thick,  the 
rise  of  temperature  in  different  parts  of  the  same  wire 
(carrying  the  same  current),  being,  for  different  thick- 
nesses, inversely  proportional  to  the  fourth  power  of  the 
diameters. 

Thus,  suppose  a  wire  at  any  point  to  become  reduced  to  JialJ 
its  diameter,  the  cross-section  will  have  an  area  £  as  great  as  in 
the  thicker  part.  The  resistance  here  will  be  4  times  as  great, 
and  the  numbet  of  heat  units  developed  will  .be  4  times  as  great 
as  in  an  equal  length  of  the  thicker  wire.  But  4  times  the 
amount  of  heat  spent  on  £  the  amount  of  taetal  will  warm  it  to 
a  degree  1 6  times  as  great,  and  16  =  24. 

For  surgical  purposes  a  thin  platinum  wire,  heated 
red-hot  by  a  current,  is  sometimes   used  instead   of  a 


CHAP,  vii.]  ELECTRICITY  AND  MAGNETISM.  333 

knife,  as,  for  example,  in  the  operation  of  amputating  the 
tongue  for  cancer.  Platinum  is  chosen  on  account  of  its 
infusibility,  but  even  platinum  wires  are  fused  by  the 
current  if  too  strong.  Carbon  alone,  of  conductors,  resists 
fusion. 

37O.  Blasting  by  Electricity. — In  consequence  of 
these  heating  effects,  electricity  can  be  applied  to  fire 
blasts  and  mines,  stout  conducting  wires  being  carried 
from  an  appropriate  battery  at  a  distance  to  a  special 
fuze,  in  which  a  very  thin  platinum  wire  is  joined  in  the 
circuit.  This  wire  gets  hot  when  the  current  flows,  and 
being  laid  amidst  an  easily  combustible  substance  to 
serve  as  a  priming,  ignites  this  and  sets  fire  to  the  charge 
of  gunpowder.  Torpedoes  can  thus  be  exploded  beneath 
the  water,  and  at  any  desired  distance  from  the  battery. 

The  special  ase  of  heat  developed  or  abstracted  by  a 
current  passing  through  a  junction  of  dissimilar  metals, 
known  as  Peltier's  effect,  is  mentioned  in  Ait.  380. 


LESSON  XXXII.—  The  Electric  Light. 

371.  The  Voltaic  Arc. — If  two  pointed  pieces  of 
carbon  are  joined  by  wires  to  the  terminals  of  a  power- 
ful voltaic  battery  or  other  generator  of  electric  currents, 
and  are  brought  into  contact  for  a  moment  and  then 
drawn  apart  to  a  short  distance,  a  kind  of  electric  flame 
called  the  voltaic  arc  is  produced  between  the  points 
of  carbon,  and  a  brilliant  light  is  emitted  by  the  white 
hot  points  of  the  carbon  electrodes.  This  phenomenon 
was  first  noticed  by  Humphry  Davy  in  1800,  and  its  ex- 
planation appears  to  be  the  following  : — Before  contact 
the  difference  of  potential  between  the  points  is  insufficient 
to  permit  a  spark  to  leap  across  even  I77^ff7  of  an  inch  of 
air-space,  but  when  the  carbons  are  made  to  touch,  a 
current  is  established.  On  separating  the  carbons  the 
momentary  extra -current  due.  to  self-induction  of  ihe 


334 


ELEMENTARY  LESSONS  ON     [CHAP.  vn. 


circuit  (Art.  404),  which  possesses  a  high  electromotive- 
force,  can  leap  the  short  distance,  and  in  doing  so 
volatilises  a  small  quantity  of  carbon  between  the  points. 
Carbon  vapour  being  a  partial  conductor  allows  the 
current  to  continue  to  flow  across  the  gap,  provided  it  be 
not  too  wide ;  but  as  the  carbon  vapour  has  a  very  high 


Fig.  137- 

resistance  it  becomes  intensely  heated  by  the  passage 
of  the  current,  and  the  carbon  points  also  grow  hot. 
Since,  however,  solid  matter  is  a  better  radiator  than 
gaseous  matter,  the  carbon  points  emit  far  more  light 


CHAP.  VIL]    ELECTRICITY  AND  MAGNETISM.  335 

than  the  arc  itself,  though  they  are  not  so  hot.  In  the 
arc  the  most  infusible  substances,  such  as  flint  and 
diamond,  melt ;  and  metals  such  as  gold  and  platinum 
are  even  vapourised  readily  in  its  intense  heat.  When 
the  arc  is  produced  in  the  air  the  carbons  slowly  burn 
away  by  oxidisation.  It  is  observed,  also,  that  particles 
of  carbon  are  torn  away  from  the  +  electrode;  which  be- 
comes hollowed  out  to  a  cup-shape,  and  some  of  these 
are  deposited  on  the  —  electrode,  which  assumes  a 
pointed  form,  as  shown  in  Fig.  137.  The  resistance  oi 
the  arc  may  vary,  according  to  circumstances,  from  0*5 
ohm  to  nearly  100  ohms.  It  is  also  found  that  the  arc 
exerts  an  opposing  -electromotive-force  of  its  own  of  about 
39  volts  when  the  arc  is  quiet,  or  1 5  volts  when  hissing. 

To  produce  an  electric  light  satisfactorily  a  minimum 
electromotive-force  of  40-50  volts  is  necessary  ;  and  as 
the  current  must  be  at  least  from  5  to  10  or  more 
amptreS)  it  is  clear  that  the  internal  resistance  of  the 
battery  or  generator  must  be  kept  small.  •  With  weaker 
.currents  or  smaller  electromotive-forces  it  is  impracticable 
to  maintain  a  steady  arc.  The  internal  resistance  of 
the  ordinary  DanielPs  or  Leclanche's  cells  (as  used  in 
telegraphy)  is  too  great  to  render  them  serviceable  foi 
producing  electric  lights.  A  battery  of  40-60  Grove's 
cells  (Art.  171)  is  efficient,  but  will  not  last  more  than 
2  or  3  hours.  A  dynamo-electric  machine  (such  as 
described  in  Art.  407  to  411),  worked  by  a  steam-engine, 
is  the  best  generator  of  currents  for  practical  electric 
lighting.  The  quantity  of  light  emitted  by  an  electric 
lamp  is  disproportionate  to  the  strength  of  the  current ; 
and  is,  within  certain  limits,  proportional  to  the  square 
of  the  heat  developed,  or  to  the  fourth  power  of  the 
strength  of  the  current. 

372.  Electric  Arc  Lamps.  — Davy  employed  wood 
charcoal  for  electrodes  to  obtain  the  arc  light.  Pencils 
of  hard  gas-carbon .  were  later  introduced  by  Foucault. 
Ui  alL  the  more  recent,  arc  lamps,  pencils  of  a  more 


336 


ELEMENTARY  LESSONS  ON     [CHAP.  vn. 


dense  and  homogeneous  artificial  coke-carbon  are  used. 
These  consume  away  more  regularly,  and  less  rapidly, 
but  still  some  contrivance  is  necessary  to  push  the 
points  of  the  carbons  forward  as  fast  as 
needed.  It  is  requisite  that  the  mechan- 
ism should  start  the  arc  by  causing  the 
pencils  to  touch  and  then  separate  them 
to  the  requisite  distance  for  the  produc- 
tion of  a  steady  arc ;  the  mechanism 
should  also  cause  the  carbons  not  only 
to  be  fed  into  the  arc  as  fast  as  they 
consume,  but  also  to  approach  or  recede 
automatically  in  case  the  arc  becomes 
too  long  or  too  short ;  it  should  further 
bring  the  carbons  together  for  an  instant 
|o  start  the  arc  again  if  by  any  chance 
arc  goes  out.  Electric  Arc  Lamps 
or  Regulators,  fulfilling  these 
conditions,  have  been  invented 
by  a  number  of  persons.  These 
may  be  classified  as  follows  : — 
(a)  Clockwork  Lamps. — Fig. 
138  shows  the  regulator  of  Fou- 
cault  as  constructed  by  Duboscq; 
in  this  lamp  the  carbon-holders 
are  propelled  by  a  train  of 
clockwork  wheels  actuated  by 
a  spring.  An  electronic: jnei 
at  the  base,  through  which  the 
current  runs,  attracts  an  arma- 
ture and  governs  the  clock- 
X3a  work.  If  the  current  is  too 

strong  the  armature  is  drawn  down,  and  the  clockwork 
draws  the  carbons  further  apart.  If  the  current  is 
weakened  by  the  resistance  of  the  arc,  the  armature  is 
drawn  upwards  by  a  spring,  and  a  second  train  of  whesls 
tomes  into  play  and  moves  the  carbons  nearer  together. 


CHAP.  vn.J  ELECTRICITY  AND  MAGNETISM.  337 

Clockwork  arc  lamps  have  also  been  devised  by  Serrin 
and  by  Crompton,  in  which  the  weight  of  the  carbon- 
holders  drive  the  clockwork  mechanism. 

(b)  Break-wheel  Lamps. — Jaspar  and   Crompton  have 
devised    mechanism  for   regulating  the  rate  of  feeding 
the    carbon    into    the    arc  by  adding    to    the    train    of 
wheels  a  break-wheel ;  the  break  which  stops  the  wheel 
being  actuated  by  a  small  electromagnet  which  allows 
the  wheel  to  run  forward  a  little  when  the  resistance  of 
the  arc  increases  beyond  its  normal  amount. 

(c)  Solenoid  Lamps. — In  this  class  of  arc  lamp  one 
of  the  carbons  is  attached  to  an  iron  plunger  capable  of 
sliding   vertically  up    or   down  inside    a  hollow   coil  or 
solenoid,  which,  being  traversed  by  the  current,  regulated 
the  position  of  the  carbons  and  the  length  of  the  arc. 
Siemens    employed    two    solenoids    acting   against    one 
another  differentially,  one  being  a  main-circuit  coil,  the 
other  being  a  shunt-circuit.      If  the  resistance  of  the  arc 
became  too  great,  more  of  the  current  flowed  past  the 
lamp  through  the  shunt-circuit,  and  caused  the  carbon- 
holders  to  bring  the  carbons  nearer  together.      Shunt- 
circuits   to   regulate  the   arc  have   also    been   used   by 
Lontin,  Brush,  Lever,  and  others. 

(</)  Clutch  Lamps. — A  somewhat  simpler  device  is 
that  of  employing  a  clutch  to  pick  up  the  upper  carbon 
holder,  the  lower  carbon  remaining  fixed.  In  this  kind 
of  lamp  the  clutch  is  worked  by  an  electromagnet, 
through  which  the  current  passes.  If  the  lamp  goes 
out  the  magnet  releases  the  clutch,  and  the  upper  carbon 
falls  by  its  own  weight  and  touches  the  lower  carbon. 
Instantly  the  current  starts  round  the  electromagnet, 
causes  it  to  act  on  the  clutch  which  grips  the  carbon- 
holder  and  raises  it  to  the  requisite  distance.  Should 
the  arc  grow  too  long  the  lessening  attraction  on  the 
clutch  permits  the  carbon -holder  to  advance  a  little. 
Hart,  Brush,  Weston,  and  Lever  employ  clutch  lamps. 

373.  Electric  Candles. — To  obviate  the  expense 


ELEMENTARY  LESSONS  ON      [CHAP.  vn. 


and  complication  of  such  regulators,  electric  candles  have 

been  suggested  by  Jablochkoff, 
Wilde,  and  others.  Fig.  139 
depicts  Jablochkoff*s  candle, 
consisting  of  two  parallel  pen- 
cils of  hard  carbon  separated 
by  a  thin  layer  of  plaster  of 
Paris  and  supported  in  an  up- 
right holder.  The  arc  plays 
across  the  summit  between  the 
two  carbon  wicks.  In  order 
that  both  carbons  may  consume 
at  equal  rates,  rapidly  alternat- 
ing currents  must  be  employed, 
which  is  disadvantageous  from, 
an  economical  point  of  view. 

374.  Incandescent  Elec  - 
trie  Lamps. — Voltaic  arcs  of 
an  illuminating  power  of  less 
than  100  candles  cannot  be 
maintained  steady  in  practice, 
and  are  uneconomical.  For 


Fig.  139. 


small  lights  it  is  both  simpler  and  cheaper  to  employ  a 
thin  continuous  wire  or  filament  of  some  infusible  con- 
ductor, heated  to  whiteness  by  passing  a  current  through 
it  Thin  wires  of  platinum  have  repeatedly  been  sug- 
gested for  this  purpose,  but  they  cannot  be  kept  from 
risk  of  fusing.  Iridium  wires  and  thm  strips  of  carbon 
have  also  been  suggested  by  many  inventors.  Edison  in 
1878  devised  a  lamp  consisting  of  a  platinum  spiral  com- 
bined with  a  short-circuiting  switch  to  divert  the  current 
from  the  lamp  in  case  it  became  overheated.  More  recently 
thin  filaments  of  carbon  have  been  employed  by  Swan, 
Edison,  Lane-Fox,  Maxim,  Crookes,  and  others  for  the 
construction  of  little  incandescent  lamps.  In  these  lamps 
the  carbon  filament  is  mounted  upon  conducting  wires, 
usually  oi  platinum,  which  pass  into  a  glass  bulb,  into 


CHAP,  vii.]  ELECTRICITY  AND  MAGNETISM.          339 


which  they  are  sealed,  the  bulbs  bfeing  afterwards  ex<» 
hausted  of  air  and  other  gases,  the  vacuum  being  made 
very  perfect  by  the  employment  of  special  mercurial 
air-pumps.  Carbon  is  better  for  this  purpose  than 
platinum  or  any  other  metal,  partly  because  of  its 
superior  infusibility  and  higher  resistance,  and  partly 
because  of  the  remarkable  property  of  carbon  of  offering 
a  lower  resistance  when  hot  than  when  cold.  This 
property,  v/hich  is  the  reverse  of  that  observed  in  metals, 
renders  it  less 
liable  to  become 
overheated. 
The  forms  of 
several  incan- 
descent lamps 
are  shown  in 
Fig.  140.  Swan 
( i )  prepares  his 
filament  from 
cotton  thread 
parchmentised 
in  sulphuric 
acid  and  after- 
wards carbon- 
ised ;  such  a 
filament  be- 
coming remark- 
ably elastic  and 
metal-like  in  the  process.  Edison  (2)  now  uses  a  thin 
flat  strip  of  carbonised  bamboo  instead  of  a  .filament. 
Maxim  (3)  uses  a  preparation  of  paper.  Lane- Fox  (4) 
and  Akester  (6)  use  prepared  and  carbonised  vegetable 
fibres.  Crookes  (5)  employs  a  filament  made  from  animal 
or  vegetable  matter  parchmentised  by  treatment  with 
cuprammonic  chloride.  The  resistance  of  such  lamps 
varies  according  to  size  and  length  of  the  filament  from 
3  to  200  ohn\s.  The  current  necessary  to  heat  the 


Fig. 


340  ELEMENTARY  LESSONS  ON     [CHAP,  vii, 

filaments  white-hot  is  usually  from  I  to  I  -3  ampere.  To 
produce  this  current  the  electromotive  force  that  must 
be  applied  is  dependent  on  the  resistance  of  the  lamp. 
Suppose  a  lamp  the  resistance  of  which  is  60  ohms  when 
cold  and  40  ohms  when  hot :  the  requisite  current  will 
be  obtained  by  applying  an  electromotive  force  of  about 
50  volts,  because  50  -7-  40  =  1-25  ampere.  The  best 
economy  is  obtained  with  very  thin  cylindrical  filaments 
of  high  resistance.  Flat  strips  of-  carbon  which  expose 
a  disproportionate  amount  of  surface,  and  thick  filaments 
in  which  the  mass  of  carbon  is  considerable,  are  open 
to  objection.  Well-made  lamps,  if  not  overheated,  will 
last  1000  to  1200  hours  before  the  filament  disintegrates. 
It  is  usual  to  group  these  lamps  in  parallel  arc  between 
the  leading  main  conductor  and  the  return  main,  so  that 
each  lamp  is  independent  of  the  others  if  the  electro- 
motive force  of  the  supply  is  constant.  The  light 
emitted  varies  according  to  the  size  of  lamp  from  2  to 
50  candles.  There  appears  to  be  some  difficulty  in 
obtaining  durable  filaments  that  will  bear  being  made 
incandescent  to  a  higher  candle  power. 

LESSON  XXXIII. — Electromotors  (Electromagnetic 
Engines'). 

375.  Electromotors. — Electromagnetic  engines,  or 
electromotors,  are  machines  in  which  the  motive  power 
is  derived  from  electric  currents  by  means  of  electro- 
magnets. In  1821  Faraday  showed  a  simple  case  of 
rotation  produced  between  a  magnet  and  a  current  of 
electricity.  In  1831  Henry,  and  in  1833  Ritchie,  COK 
structed  electromagnetic  engines  producing  rotation  by 
electromagnetic  means.  Fig.  141  shows  a  modification 
of  Ritchie's  electromotor.  An  electromagnet  DC,  is 
poised  upon  a  vertical  axis  betv/een  the  poles  of  a  fixed 
magnet  (or  electromagnet)  SN.  A  current,  generated 
by  a  suitable  battery,  is  carried  by  wires  which  terminate 


CHAP,  vii.]   ELECTRICITY  AND  MAGNETISM.          341 


in  two  mercury-cups,  A,  B,  into  which  dip  the  ends  of 
the  coil  of  the  movable  electromagnet  CD.  When  a 
current  traverses  the  coil  of 
CD  it  turns  so  as  to  set  itself 
in  the  line  between  the  poles 
NS,  but  as  it  swings  round, 
the  wires  that  dip  into  the  mer- 
cury-cups pass  from  one  cup 
to  the  opposite,  so  that,  at  the 
moment  when  C  approaches  S, 
the  current  in  CD  is  reversed, 
and  C  is  repelled  from  S  and 
attracted  round  to  N,  the  cur- 
rent through  CD  being  thus 
reversed  every  half  turn.  In 
larger  electromotors,  the  mer- 
cury-cup arrangement  is  replaced 
by  a  commutator,  consisting  of 
a  brass  ring,  slit  into  two  or 
more  parts,  and  touched  at  Fis-  -141-. 

opposite  points  by  a  pair  of  metallic  springs  or  "  contact 
brushes." 

In  another  form  of  electromotor,  devised  by  Froment, 
bars  of  iron  fixed  upon  the  circumference  of  a  rotating 
cylinder  are  attracted  up  towards  an  electromagnet,  in 
which  the  current  is  automatically  broken  at  the  instant 
when  each  bar  has  come  close  up  to  its  poles.  In  a  third 
kind,  an  electromagnet  is  made  to  attract  a  piece  of  soft 
iron  alternately  up  and  down,  with  a  motion  like  the 
piston  of  a  steam-engine,  which  is  converted  by  a  crank 
into  a  rotatory  motion.  In  these  cases  the  difficulty 
occurs  that,  as  the  attraction  of  an  electromagnet 'falls  off 
nearly  in  inverse  proportion  to  the  square  of  the  distance 
from  its  poles,  the  attracting  force  can  only  produce 
effective  motion  through  very  small  distances. 

The  dynamo-electric  machines  of  Gramme,  Siemens, 
and  others,  described  in  Ail-.  407  to  41 i,  will  also,  work 


342  ELEMENTARY  LESSONS  ON      [CHAP.  vn. 

as  electromotors,  and,  indeed,  are  the  most  efficient  of 
electromagnetic  engines. 

In  1839  Jacobi  propelled  a  boat  along  the  river  Neva 
at  the  rate  of  2^  miles  per  hour  with  an  electromagnetic 
engine  of  about  one  horse-power,  worked  by  a  battery  of 
64  large  Grove's  cells. 

In  1882  an  iron  screw-boat  capable  of  carrying  12 
persons,  and  driven  by  two  Siemens'  dynamos,  with  a 
power  of  about  3  horse-power,  the  electricity  being  fur- 
nished by  45  accumulators  of  the  Sellon-Volckmar  type, 
has  been  worked  upon  the  Thames  at  a  speed  of  8  miles 
per  hour. 

Electric  railways  on  which  trains  are  propelled  by 
power  furnished  by  dynamo-electric  generators  stationed 
at  some  fixed  point,  and  communicating  with  the  electro- 
magnetic machinery  of  the  train  either  by  the  rails  or  by 
a  special  conductor,  have  been  constructed  by  Siemens 
in  Berlin,  and  by  Edison  in  Menlo  Park. 

376.  Electric   Transmission   of  Power   to   a 
distance.  —  The    increasing    use    of    dynamo -electric 
machines  for  electric  lighting  has  revived  the  problem  of 
transmitting  power  to  a  distance  by  electrical  means, 
and  so  utilising  waste  water-power.     A  mountain  stream 
may  be   made  to  turn  a  water-wheel  or  turbine,   and 
drive  a   dynamo -electric    machine,   thereby  generating 
currents  which  can  be  conveyed  by  wires  to  an  electro- 
motor at  a  distant    point,   and  there  reconverted  into 
mechanical  power     Whether  such  transmission  is  profit- 
able or  not  depends  on  the  efficiency  of  the  machines 
employed. 

377.  Theory  of  Efficiency  of  Electromotors. — 
If  a  galvanometer  be  included  in  a  circuit  with  a  battery 
and  an  electromotor,  it  is  found  that  the  current  is  weaker 
when  the  electromotor  is  working  than  when  the  electro- 
motor is  standing  still,  and  that  the  faster  the  electromotor 
runs  the  weaker  does  the  battery  current  become.     This 
is  due  to  electromagnetic  induction  (Art.  391)  between  the 


CHAP.  vii.]  ELECTRICITY  AND  MAGNETISM.  343 

moving  and  fixed  parts  of  the  electromotor,  which,  as  it 
spins  round,  generates  a  back-current.  The  electromotive- 
force  due  to  this  inductive  action  increases  with  the  speed 
of  the  electromotor,  so  that  the  back-current  is  strongest 
when  it  runs  fastest.  If  the  motor  be  loaded  so  as  to 
do  work  by  moving  slowly  against  considerable  forces,  the 
back-current  will  be  small,  and  only  a  small  proportion 
o£  the  energy  of  the  current  will  be  turned  into  useful 
work.  If  it  be  set  to  run  very  quickly,  so  as  to  generate 
a  considerable  back-current,  it  will  utilise  a  larger  pro- 
portion of  the  energy  of  the  direct  current,  but  can  only 
run  fast  enough  to  do  this  if  its  load  be  very  light. 
Jacobi  calculated  that  the  practical  efficiency  lay  between 
these  two  extremes,  and  that  an  electromotor  would  turn 
the  energy  of  a  battery  into  work  in  the  most  effective 
way  when  it  was  allowed  to  do  its  work  at  such  a  speed 
that  the  battery  current  was  thereby  reduced  to  half  its 
strength.  This  is  indeed  true  if  it  be  desired  to  do  the 
work  at  the  quickest  possible  rate.  But  where  economy 
in  working  is  desired,  and  when  it  is  not  needful  to  get 
through  the  work  as  rapidly  as  possible,  or  to  consume 
materials  in  the  battery  at  a  great  rate,  then  a  higher 
economic  efficiency  will  be  attained  by  making  the  electro- 
motor do  lighter  work  and  spin  at  a  greater  speed ;  for 
if  the  electromotive-force  of  the  battery  be  E  volts  ^  and 
the  counter  electromotive-force  of  the  motor  while  running 
be  e  volts,  then  the  efficiency  of  the  motor  (that  is  to 
say,  the  ratio  which  the  work  it  takes  up  from  the  cur- 
rent bears  to  the  whole  energy  of  the  current)  will  be 
equal  to  •-  Now  if  the  motor  be  allowed  to  run  more 
quickly  e  will  increase  proportionately,  and  if  it  runs 
very  quickly  e  may  become  very  nearly  equal  to  E  ;  that 
is  to  say,  the  motor  will  utilise  very  nearly  all  the  energy 
of  the  current.  But  since,  by  Ohm's  law,  the  current  is 
—  -^,  it  follows  that  if  e  is  very  nearly  as  great  as  E, 
the  current  will  be  reduced  to  a  small  fraction  of  its 
original  strength.  The  materials  of  the  battery  will  be 


344  ELEMENTARY  LESSONS  ON      [CHAP.  VH. 

more  slowly  used,  and  it  will  take  a  longer  time  to  do 
the  total  amount  of  the  work,  but  the  percentage  of 
energy  of  the  current  turned  into  work  will  be  higher. 
A  good  modern  dynamo-electric  machine  (Art.  408)  used 
as  a  motor  can  attain  an  efficiency  of  over  90  per  cent. 

378.  Cost  of  Working.  —  The  cost  of  working 
electromotors  by  batteries  is  great.  A  pound  of  zinc 
contains  only  about  \  as  much  potential  energy  as  a 
pound  of  coal,  and  it  costs  more  than  twenty  times  as 
much  :  the  relative  cost  for  equal  amounts  of  energy  is 
therefore  about  120  :  i.  But,  as  shown  above,  an  elec- 
tromagnetic engine  .will  turn  8  5  per  cent  of  the  electric 
energy  into  work,  while  even  good  steam-engines  only 
turn  about  10  to  20  per  cent  of  the  energy  of  their  fuel 
into  work,  small  steam-engines  being  even  less  efficient. 
But,  reckoning  electromagnetic  engines  as  being  5  times 
as  "efficient"  as  steam-engines  of  equal  power,  the 
necessary  zinc  is  still  24  times  as  dear  as  the  equivalent 
amount  of  coaL  This  calculation  does  not  take  into 
account  the  cost  of  acids  of  the  batteries.  In  fact, 
where  strong  currents  are  wanted,  batteries  are  aban- 
doned in  favour  of  dynamo-electric  machines,  worked  by 
steam  or  water  power,  or  by  gas-engines. 

In  the  case  of  transmission  of  power,  as  in  the  preced- 
ing paragraph,  the  expense  may  be  far  smaller  if  the 
original  water-power  costs  little.  The  dynamo-machine 
may  turn  90  per  cent  of  the  mechanical  power  into  the 
energy  of  electric  currents,  and  the  electromotor  may 
convert  back  85  per  cent  of  the  current  energy  (or  76 
per  cent  of  the  original  power)  into  work. 

378.  (bis)  Calculation  of  Electric  Power. — The 
mechanical  work  of  a  current  may  be  calculated  as 
follows  :  A  current  whose  strength  is  C  conveys  through 
the  circuit  in  /  seconds  a  quantity  of  electricity  =  C/. 
But  the  number  of  ergs  of  work  W,  done  by  a  current 
is  equal  to  the  product  of  the  quantity  of  electricity  into 
the  difference  of  potentials  E  through  which  it  is  irans- 


CHAP,  vit.]  ELECTRICITY  AND  MAGNETISM  345 

ferred  (Art.  367),  provided  these  latter  are  expressed  in 
"  absolute  "  C.G.S.  units  ;  or 

C/E=W 

Now  if  W  ergs  of  work  are  done  in  /  seconds,  the  rate  of 
working  is  got  by  dividing  W  by  t;  whence 


If  C  and  E  are  expressed  in  amperes  and  volts  respec- 
tively, and  it  is  desired  to  give  the  rate  of  working  in 
horse  -power,  it  must  be  remembered  that  I  ampere  = 
lo'1  C.G.S.  units  of  current;  that  I  volt  =  io8  C.G.S. 
units  of  E.M.F.  ;  and  that  I  horse-power  (as  defined  by 
Watt)  =550  foot-pounds  per  second  =  76  kilogramme- 
metres  per  second  =  76  x  io5  gramme-centimetres  per 
second  =  746  x  io7  ergs  per  second,  whence 

CaJsiu3Lx_EIM.  Of  doing  work  in  H.-P. 

746 

For  example,  to  find  the  rate  at  which  actual  work  is 
consumed  in  an  electric  lamp  :  measure  the  whole  current 
in  amperes  ;  measure  the  difference  of  potential  between 
the  terminals  of  the  lamp  in  volts;  multiply  them  to- 
gether and  divide  by  746  ;  the  result  will  be  the  number 
of  horse-power  used  up  in  the"  lamp  :  or  the  rule  may  be 
written  thus  :  — 

H-P  =  CE  x  0-00134. 

A  convenient  "  electric  POIV  er-ineter  "  may  be  made  of 
an  electrodjnamometer  (Art.  336)  having  the  fixed  coil 
of  thick  wire  to  receive  the  whole  current,  and  having 
the  movable  coil  of  many  turns  of  thin  wire  arranged 
as  a  shunt  to  the  lamp  or  dynamo  whose  power  is  to  be 
measured. 

It  has  been  proposed  by  Preece  and  by  Siemens  to 
call  the  unit  of  electric  power  (/.<?.  one  ampere  working 
through  one  volt}  a  watt.  One  horse-power  will  equal 
746  watts. 


3  A 


346  ELEMENTARY  LESSONS  ON     [CHAP,  vm 


CHAPTER  VIII. 

THERMO-ELECTRIC  ITY. 

LESSON  XXXIV. — Thenno-Electric  Currents. 

379.  In  1822  Seebeck  discovered  that  a  current  may 
be  produced  in  a  closed  circuit  by  heating  a  point  of 
contact  of  two   dissimilar  metals.     Thus,  if  a  piece  of 
bismuth   and  a  piece  of  antimony  be  soldered  together, 
and   their    free    ends    be    connected    with    a    short -coil 
galvanometer,  it  is  found  that  if  the  junction  be  warmed 
to  a  temperature  higher  than   that  of  the  rest  of  the 
circuit,  a  current  flows  whose  direction  across  the  heated 
point  is  from  bismuth  to  antimony,  the  strength  of  the 
current  being  proportional  to  the  excess  of  temperature. 
If  the  junction  is  cooled  below  the  temperature  of  the 
rest  of  the  circuit  a  current  in  the  opposite  direction  is 
generated.     The    electromotive -force    thus    set    up   will 
maintain  a  constant   current  so  long  as  the   excess  of 
temperature  of  the  heated  point  is  kept  up,  heat  being 
all  the  while  absorbed  in  order  to  maintain  the  energy  of 
the  current.     Such  currents  are  called  Thermo-electric 
currents,  and  the  electromotive -force  producing  them 
is  known  as  Thermo-electromotive-force. 

380.  Peltier  Effect.  —  In   1834  Peltier  discovered 
a  phenomenon  which  is  the  converse  of  that  discovered 
by  Seebeck.      He  found  that  if  a  current  of  electricity 
from  a  battery  be  passed  through  a  junction  of  dissimilar 
metals  the  junction,  is  either  heated  or  cooled,  according 


CHAP.  vni.J    ELECTRICITY  AND  MAGNETISM.         347 

to  the  direction  of  the  current.  Thus  at  current  which 
passes  through  a  bismuth-antimony  pair  in  the  direction 
from  bismuth  to  antimony  absorbs  heat  in  passing  the 
junction  of  these  metals,  and  cools  it ;  whereas,  if  the 
current  flow  from  antimony  to  bismuth  across  the 
junction  it  evolves  heat,  and  the  junction  rises  in  tem- 
perature. 

This  phenomenon  of  heating  "(or  cooling)  by  a  current, 
where  it  crosses  the  junction  -of  two  dissimilar  metals 
(known  as  the  "  Peltier  effect,"  to  distinguish  it  from  the 
ordinary  heating  of  a  circuit  where  it  offers  a  resistance 
to  the  current,  which  is  sometimes  called  the  "Joule 
effect "),  is  utterly  different  from  the  evolution  of  heat  in 
a  conductor  of  high  resistance,  for  (a)  the  Peltier  effect 
is  reversible^  the  current  heating  or  cooling  the  junction 
according  to  its  direction,  whereas  a  current  meeting 
with  resistance  in  a  thin  wire  heats  it  in  whichever 
direction  it  moves  ;  and  (b)  the  amount  of  heat  evolved 
or  absorbed  in  the  Peltier  effect  is  proportional  simply 
to  the  strength  of  the  current,  not  to  the  square  of  that 
strength  as  the  heat  of  resistance  is. 

The  complete  law  of  the  heat  developed  in  a  circuit  will 
therefore  require  to  take  into  account  any  Peltier  effects  which 
may  exist  at  metal  junctions  in  the  circuit.  If  the  letter  P 
stand  for  the  difference  of  potential  due  to  the  heating  of  the 
junction,  expressed  as  a  fraction  of  a  volt,  then  the  complete 
law  of  heat  is 

H  =  0-24  x  (C2R/  +  PC/) 

which  the  student  should  compare  with  Joule's  law  in  Art.  367. 
The  quantity  called  P  is  also  knoVn  as  the  coefficient  of  tk: 
Peltier  effect ;  it  has  different  values  for  different  pairs  of  metals, 
and  is  numerically  equal  to  the  number  of  ergs  of  work  which 
are  the  dynamical  equivalent  of  the  heat  evolved  at  a  junction 
of  the  particular  metals  by  the  passage  of  one  amp} re  of  electricity 
through  the  junction. 

381.  Thermo-electric  Laws. — The  thermo-electric 
properties  of  a  circuit  are  best  studied  by  reference  to 
the  simple  circuit  of  Fig.  142,  which  represents  a 


348 


ELEMENTARY  LESSONS  ON    [CHAT.  vm. 


Fig.  142. 


bismuth-antimony  pair  united  by  a  copper  wire.  Volta's 
law  (Art.  72)  concerning  the  difference  of -potentials 
due  to  contact  would  tell  us  that  when  all  are  at  one 

temperature  the  dif- 
ference of  poten- 
tials between-^bis- 
inuth  and  copper 
in  one  direction 
is  equal  to  the  sum 
of  the  differences 
between  bismuth 
and  antimony,  and 
between  antimony 
and  copper  in  the 
other  direction,  and  that  hence  there  would  be  equilibrium 
between  the  opposing  and  equal  electromotive -forces. 
But  when  a  junction  is  heated  this  equilibrium  no  longer 
exists  and  Yolta's  law  ceases  to  be  true.  The  new 
electromotive-force  set  up  at  the  heated  junction  is  found 
to  obey  the  following  laws  : — 

(i.)  The  thermo -electromotive-force  is,  for  tJie  same 
pair  of  metals^  proportional  (even  through  con- 
siderable ranges  of  temperature)  to  the  excess,  of 
temperature  of  the  junction  over  the  rest  of  the 
circuit. 

(ii.)  The  total  thermo-electromotive -force  in  a  circuit 
is  the  sum  of  all  the  separate  thermo-eJeclronwtlve- 
forces  at  the  various  junctions. 

It  follows  from  this  law  that  the  various  metals  can  be 
arranged,  as  Seebeck  found,  in  a  series,  according  to 
their  thermo-electric  power,  eaclvone  in  the  series  being 
thermo-electrically  positive  (as  bismuth  is  to  antimony) 
toward  one  lower  down.  The  following  is  the  thermo- 
electric series  of  metals,  together  with  th2  differenceb 
of  potentials  (in  microvolts)  which  they  exhibit  with  a 
difference  of  temperature  of  i°C,  lead  being  regarded  as 
the  standard  zero  me.taL 


CHAP,  viii.]  ELECTRICITY  AND  MAGNETISM.         349 

+  Bismuth     .          .         .         .  89  to  97 

German-silver     .         .         .  I1 '7  5 

Lead          ...         .  O 

Platinum  .  .  .  «  —  0*9 
Zinc  ".  .  .  .  -  37 
Copper  .  .  .  "  .  —  3*8 

Iron -  ITS 

—  Antimony  .         .         .         •     —  22*6  to  —  26*4 
A  very  small  amount  of  impurity  may  make  a  great 
difference  in  the  thermo-electric  power  of  a  metal,  and 
some  alloys,  and   some    of  the    metallic    sulphides,    as 
galena,  exhibit  extreme  thermo-electric  power. 

The  electromotive -forces  due  to  heating  single  pairs 
of  metals  are  very  small  indeed.  If  the  junction  of  a 
copper-iron  pair  be  raised  i°C  above  the  rest  of  the 
circuit  its  electromotive-force  is  only  13*7  millionths  of  a 
volt  (i.e.  137  microvolts).  That  of  the  more  powerful 
bismuth-antimony  pair  is  for  i°C,  about  117  microvolts. 

382.  Thermo-electric  Inversion. — Gumming  dis- 
covered that  in  the   case  of  iron  and  other  metals'  an 
inversion   of  their  thermo-electric  properties  may  take 
place  at  a  high  temperature.      In  the  case  of  the  copper- 
iron  pair  the  temperature  of  280°  is  a  neutral  point ; 
below  that  temperature  the  current  flows  through  the 
hotter  junction  from  the  copper  to  the  iron  ;  but  when 
the  circuit  is   above  that  temperature   iron  is   thermo- 
electrically  positive  to  copper. 

383.  Thermo-electric   Diagram.  —  The  facts    of 
thermo-electricity    are    best    studied    by   means    of  the 
diagram  (Fig.  143)  suggested  by  Sir  W.  Thomson  and 
constructed  by  Professor  Tait.      The  horizontal  divisions 
represent  temperatures,  the  vertical  distances  differences 
of  potential  divided  by  absolute  temperatures,  on  a  scale 
of  millionths  of  volts  per  degree.     These  differences  are 
measured  with    respect    to    the    metal    lead,    which    is 
taken  as  the  standard  of  zero  at  all  temperatures,  because, 
while  with  other  metals  there  appears  to  be  a  difference 
of  potentials  between  the  metal  hot  and  the  same  metal 


35° 


ELEMENTARY  LESSONS  ON    [CHAP.  vm. 


cold,  hot  lead  brought  into  contact  with  cold  lead  shows 
no  perceptible  difference  of  potential. 


+  5 


LEAD 


-5 


-10 


0° 


400* 


g.  143- 

An  example  will  illustrate  the  usefulness  of  the  diagram.  Let 
a  circuit  be  made  by  uniting  at  both  ends  a  piece  of  iron  and  a 
piece  of  copper  ;  and  let  the  two  junctions  be  kept  at  o°  and 
1 00°  respectively  by  melting  ice  and  boiling  water.  Then  the 
total  electromotive-force  round  the  circuit  is  represented  by  the 
area  a,  O,  -15,  b.  The  slope  of  the  lines  for  the  various  metals 
represents  the  property  referred  to  above,  of  an  electromotive- 
force  between  differently  heated  portions  of  the  same  metal 
accompanied  by  an  absorption  or  evolution  of  heat  when  the 
current  flows  from  a  hotter  to  a  colder  portion  of  the  same 
metal.  This  effect,  known  as  the  Thomson  effect  from  its 
discoverer  Sir  W.  Thomson,  is  opposite  in  iron  to  what  it  is 
in  copper  or  zinc.  In  copper,  when  a  current  of  electricity  flows 
from  a  hot  to  a  cold  point,  it  evolves  heat  in  the  copper,  and  it 
absorbs  heat  when  it-  flows  from  a  cold  point  to  a  hot  point  in 
the  copper.  In  iron  a  current  flowing  from  a  hot  point  to  a^ 
cold  point  absorbs  heat. 

384.  Thermo-electric  Piles.— IQ  prderjo  increase 


CHAP,  viii.]  ELECTRICITY  AND  MAGNETISM.         351 

the  electromotive-force  of  thermo-electric  pairs  it  is  usual 
to  join  a  number  of  pairs  of  metals  (preferably  bismuth 
and  antimony)  in  series,  but  so  bent  that  the  alternatt 
junctions  can  be  heated  as  shown  in  Fig.  144  at  B  B  B, 


Fig.  144. 

ivhiLt  the  other  set  A  A  A  are  kept  cool.  The  various 
electromotive-forces  then  all  act  in  the  same  direction, 
and  the  current  is  increased  in  proportion  to  the  number 
of  pairs  of  junctions.  Powerful  thermo-electric  batteries 
have  been  made  by  Clamond, — an  iron-galena  battery 
of  1 20  pairs  affording  a  strong  current;  but  it  is 
extiemely  difficult  to  maintain  them  in  effecthe  action 
for  long,  as  they  fail  after  continued  use,  probably 
o\\  ing  to  a  permanent  molecular  change  at  the  junctions. 
In  the  hands  of  Melloni  the  thermo-electric  pile  or 
thermopile,  constructed  of  many  small  pairs  of  anti- 
mony and  bismuth  united  in  a  compact  form,  proved  an 
excellent  electrical  thermometer  when  used  in  conjunction 
with  a  sensitive  short-coil  astatic  gahanometer  like  that 
of  Fig.  88.  For  the  detection  of  excessively  small 
differences  of  temperature  the  thermopile  is  an  invaluable 
instrument,  the  currents  being  propoitional  to  the  differ- 


352 


ELEMENTARY  LESSONS  ON    [CHAP.  vm. 


ence  of  temperature  between  the  hotter  set  of  junctions 
on  one  face  of  the  thermopile  and  the  cooler  set  on  the 
other  face.  The  arrangement  of  the  thermopile  and 
galvanometer  for  this  purpose  is  shown  in  Fig.  145. 


us 


CHAP,  ix.]   ELECTRICITY  AND  MAGNETISM.  353 


CHAPTER   IX. 

ELECTRO-OPTICS. 

LESSON  XXXV.-—  General  Relations  between  Ugh* 
and  Electricity. 

385.  Of  late  years  several  important  relations  have 
been   observed   between   electricity   and  light.     These 
relations  may  be  classified  under  the  following  heads : — 

(i.)  Production  of  double  refraction  by  dielectric  stress. 

(ii.)  Rotation  of  plane  of  polarisation  of  a  ray  of  light 

on  traversing  a  transparent  medium  placed  jn  a 

magnetic  field,  or  by  reflection  at  the  surface  of  a 

magnet 

(in.)  Change    of   electric    resistance,    exhibited    by 

selenium  and  other  bodies  during  exposure  to  light 

(iv.)  Relation  between  refractive  index  and  dielectric 

capacity  of  transparent  bodies. 

It  was  announced  by  Mrs.  Somerville;  by  Zantedeschi,  and 
others,  that  steel  needles  could  be  magnetised  by  exposing 
portions  of  them  to  the  action  of  violet  and  ultra-violet  rays 
of  light ;  the  observations  were,  however,  erroneous. 

386.  Electrostatic  Optical  Stress. — In  1875  Dr. 
Kerr  of  Glasgow  discovered  that  glass  when  subjected  to 
a  severe  electrostatic  stress  undergoes  an  actual  strain, 
which  can  be  observed  by  the  aid  of  a  beam  of  polarised 
light      In  the  original  experiment  two  wires  were  fixed 
into  holes  drilled  in  a  slab  of  glass,  but  not  quite  meeting, 


354  ELEMENTARY  LESSONS  ON      [CHAPO  ix, 

so  that  when  these  were  placed  in  connection  with  the 
terminals  of  an  induction  coil  or  of  a  Holtz  machine  the 
accumulating  charges  on  the  wires  subjected  the  inter- 
vening dielectric  to  an  electrostatic  stress.  The  slab 
when  placed  between  two  Nicol  prisms  as  polariser  and 
analyser1  exhibited  double  refraction.  The  behaviour  ol 
the  glass  was  as  if  it  had  been  subjected  to  a  pull  along 
the  direction  of  the  electric  force,  /.«<?.,  as  if  it  had  ex- 
panded along  the  lines  of  electrostatic  induction.  Later, 
be  found  that  bisulphide  of  carbon  and  other  insulating 
liquids  exhibit  similar  phenomena,  but  that  of  these  the 
fatty  oils  of  animal  and  vegetable  origin  exhibited  an 
action  in  the  negative  direction,  as  if  they  had  contracted 
along  the  lines  of  induction.  It  is  found  that  the 
quantify  of  optical  effect  (i.e.,  the  difference  of  retardation 
betureen  the  ordinary  and  extraordinary  rays)  per  unit 
thickness  of  the  dielectric  is  proportioned  to  the  square  of 
the  resultant  electric  force.  The  axis  of  double  refraction 
is  along  the  line  of  the  electric  force.  Quincke  has 
pointed  otit  that  these  phenomena  can  be  explained,  by 
the  existence  of  electrostatic  expansions  and  contractions, 
stated  in  Art.  273. 

387.  Magneto-optic  Rotation  -of  the  Plane  of 
Polarisation  of  a  Bay  of  Light. — A  ray  of  light 
is  said  to  be  polarised  if  the  vibrations  take  place  in  one 
plane.  Ordinary  light  can  be  reduced  to  this  condition 
by  passing  it  through  a  suitable  polarising  app'aratus 
(such  as  a  Nicol  prism,  a  thin  slice  of  tourmaline  crystal. 
etc.)  In  1845  Faraday  discovered  that  a  ray  polarised 
in  a  certain  plane  can  be  twisted  round  by  the  action 
of  a  magnet,  so  that  the  vibrations  are  executed  in  a 
different  plane.  The  plane  in  which  a  ray  is  polarised 
can  be  detected  by  observing  it  through  a  second  Nicol 
prism  •  (or  tourmaline),  for  each  such  polariser  is  opaque 
to  rays  polarised  in  a  plane  at  right  angles  to  that  plane 

•  The  student  is  referred  to  Prof.  Balfour  Stewart's  Lessons  on  V.lemr.nt- 
r  f  Physics  for  further  information  concerning  the  properties  of  polarised  light. 


CHAP,  ix,]    ELECTRICITY  AND  MAGNETISM.  355 

in  which  it  would  itself  polarise  light.  Faraday  caused 
a  polarised  ray  to  pass  through  a  piece  of  a  certain 
"  heavy  glass "  (consisting  chiefly  of  bora'fe  of  lead), 
lying  in  a  powerful  magnetic  field,  between  the  poles 
of  a  large  electromagnet,  through  the  coils  of  which  a 
current  could  be  sent  at  pleasure.  The  emerging  ray 
traversed  a  second  Nicol  prism  which  had  been  turned 
round  until  all  the  light  was  extinguished.  In  this  posi- 
tion its  own  plane  of  symmetry  was  at  right  angles  to  the 
plane  of  polarisation  of  the  ray.  On  completing  the  cir- 
cuit, light  was  at  once  seen  through  the  analysing  Nicol 
prism,  proving  that  the  ray  had  been  twisted  round  into 
a  new  position,  in  which  its  plane  of  polarisation  was  no 
longer  at  right  angles  to  the  plane  of  symmetry  of  the 
analyser.  But  if  the  analysing  Nicol  prism  was  itself 
turned  round,  a  new  position  could  be  found  (at  right 
angles  to  the  plane  of  polarisation  of  the  ray)  at  which 
the  light  was  once  more  extinguished.  The  direction  oj 
the  magneto-optic  rotation  of  the  plane  of  polarisation  is 
the  same  (for  diamagnetic  media)  as  that  in  which  the 
current  flows  which  produces  the  magnetism.  Verdet, 
who  repeated  Faraday's  experiments,  using  powerful 
electromagnets  of  the  form  shown  in  Fig.  127,  dis- 
covered the  important  law  that,  with  a  given  material. 
the  amount  of  rotation  is  proportional  to  the  strength  oj 
the  magnetic  force  H.  In  case  the  rays  do  not  pass 
straight  along  the  direction  of  the  lines  of  force  (which 
is  the  direction  of  maximum  effect),  the  amount  of  rota- 
tion is  proportional  to  the  cosine  of  the  angle  (3  between 
the  direction  of  the  ray  and  the  lines  of  force.  It  is  also 
proportional  to  the  length  I  .of  the  material  through 
which  the  rays  pass.  These  laws  are  combined  in  the 
equation  for  the  rotation  d ; 

6  =  iv  •  H  •  cos  {3  -  /, 

where  w  is  a  coefficient  which  represents  the  specific 
magnetic  rotatory  power  of  the  given  substance,  and  is 
known  as  "  Verdefs  cons' ant."  Now,  H  -cos  8  is  the 


356  ELEMENTARY  LESSONS  ON       [CHAP.  ix. 

resolved  part  of  the  magnetic  force  in  the  direction  of 
the  rtiy  ;  and  H  •  cos  jS  •  /  is  the  difference  of  magnetic 
potential1  between  the  point  A  where  the  ray  enters  and 
B  where  it  leaves  the  medium.  Hence  w,  the  coefficient 
of  specific  magnetic  rotatory  power,  is  found  by  divid- 
ing the  observed  angular  rotation  by  the  difference  of 
magnetic  potential  between  the  points  where  the  ray 
enters  and  leaves  the  medium  ;  or 

e 


Different  substances  possess  different  magnetic  rotatory 
powers.  For  diamagnetic  substances  the  coefficient  is 
usually  positive;  but  in  the  case  of  many  magnetic 
substances,  such  as  solutions  of  ferric  chloride,  has  a 
negative  value ;  (i.e.  in  these  substances  the  rotation  is 
in  the  opposite  direction  to  that  in  which  the  magnetising 
current  flows).  The  phenomenon  discovered  by  Hall 
(Art.  337)  appears  to  be  intimately  related  to  the 
phenomenon  of  magneto-optic  rotation. 


Bisulphide  of  Carbon 
Water     .... 
Heavy  glass    . 

Coefficient  of  Specific 
f     Magnetic  Rotation, 
(Verdet's  Constant  in  C.  G.  S.) 

Magnetic 
Rotatory 
Power. 

i'5235  x  io~B 
•4693  x  io~5 
2-665    x  10~5 

I'OOO 
•308 
I  '422 

It  is  convenient,  for  purposes  of  reference,  to  take  the 
rotatory  power  of  bisulphide  of  carbon  as  unity.  Careful 
measurements  executed  by  J.  .E.  H.  Gordon  have  shown 
that  the  rotatory  power  of  bisulphide  of  carbon,  thus 
assumed  as  a  standard,  must  be  multiplied  by  1*5235  x 
io~5  to'  reduce  it  to  C.  G.  S.  measure  ;  for  he  finds  that 

1  For  force  X  length  —  work',  and  the  work  done  in  bringing  a  unit 
magnetic  pole  from  A  to  B  against  the  magnetic  force  measures  ih? 
difference  of  magnetic  potential.  See  Art.  310  (e). 


CHAP,  ix.]  ELECTRICITY  AND  MAGNETISM..          357 

this  is  the  number  of  radians  through  which  a  polarised 
ray  of  green  light  (of  thallium  flame)  will  be  rotated  by 
traversing  unit  difference  of  potential.  For  rays  of 
different  colours  the  rotation  is  not  equal,  but  varies 
(very  nearly)  inversely  as  the  square  of  the  wave-length ; 
the  rotation  by  bisulphide  of  carbon  of  red,  green,  and 
blue  light  (rays  "C,"  "E,"  and  "G"),  being  respectively 
as  -60,  i  -oo,  and  I  '65.  H.  Becquerel,  who  gave  this  law, 
also  found  that  for  substances  of  similar  nature  the  rota- 
tion depends  on  the  refractive  index,  but  in  rather  a  com- 
plicated relation,  being  proportional  to  ^  (jj?  —  i) ; 
where  /u,  is  the  refractive  index. 

Gases  also  rotate  the  plane  of  polarisation  qf  light  in 
a  magnetic  field  with  varying  amounts;  coal-gas 'and 
carbonic  acid  being  more  poweiful  than  air  or  hydiogen; 
oxygen  and  ozone  being  negative.  The  rotation  is  in  all 
cases  very  slight,  and  varies  for  any  gas  in  piopoition  to 
the  density — that  is  to  the  quantity  of  gas  traversed.  H. 
Becqneiel  has  lately  shown  that  the  plane  of  the  natural 
polarisation  of  the  sky  does  not  coincide  with  the  plane 
of  the  sun,  but  is  rotated  by  the  influence  of  the  earth's 
magnetism  through  an  angle  which,  however,  only  reached 
59'  of  arc  at  a  maximum  on  the  magnetic  meridian. 

388.  Photo  •  magnetic  Properties  of  Iron.  —  Dr.  Kerr 
showed  in  1877  that  a  ray  of  polarised  light  is  also  rotated 
when  reflected  at  the  surface  of  a  magnet  or  electromagnet. 
When  the  light  is  reflected  at  a  pole  tlie  plane  of  polarisation  is 
turned  in  a  direction  contrary  to  that  in  which  the  magnetising 
current  flows.  If  the  light  is  reflected  at  a  point  on  the  side  of 
the  magnet  it  is  found  that  when  the  .plane  of  polarisation  is 
parallel  to  the  ^lane  of  incidence  the  rotation  is  in  the  same 
direction  as  that  of  the  magnetising  current ;  but  that,  when  the 
plane  of  polarisation  is  perpendicular  to  the  plane  of  incidence, 
the  rotation  is  in  the  same  direction  as  that  of  the  magnetising 
current  only  when  the  incidence  exceeds  75°. 

Kundt  showed  in  1884  that  a  film  of  metallic  iron  so  thin  as 
lo  be  transparent,  placed  across  the  lines  of  force  of  the  magnetic 
field,  rotates  the  plane  of  polarisation  of  transmitted  lighi 
strongly  in  the  direction  in  which  the  magnetising  current  flow 


358  ELEMENTARY  LESSONS  ON       [CHAP.  ix. 

389.  Photo-voltaic  Properties  of  Selenium.— 
In  1875  Willoughby  Smith  discovered  that  the  metal 
selenium  possesses  the  abnormal  property  of  changing 
its  electric  resistance  under  the  influence  of  light. 
Ordinary  fused  or  vitreous  selenium  is  a  very  bad 
conductor ;  its  resistance  being  nearly  forty -thousand- 
million  (3 '8  x  io10)  times  as  great  as  that  of  copper. 
When  carefully  annealed  (by  keeping  for  some  hours  at 
a  temperature  of  about  22o°C,  just  below  its  fusing 
point,  and  subsequent  slow  cooling),  it  assumes  a  crystal- 
line condition,  in  which  its  electric  resistance  is  consider- 
ably reduced.  In  the  latter  condition,  especially,  it  is 
sensitive  to  light.  Prof.  W.  G.  Adams  found  that  green- 
ish-yellow rays  were  the  most  effective.  He  also  showed 
that  the  change  of  electric  resistance  varies  directly  as 
ttie  square  root  of  the  Humiliation,  and  that  the  resist- 
ance is  less  with  a  •  high  electromotive-force  than  a 
low  one.  Lately,  Prof.  Graham  Bell  and  Mr.  Sumner 
Tainter  have  devised  forms  of  "  selenium  cells,"  in  which 
the  selenium  is  formed  into  narrow  strips  b.etween  the 
edges  of  broad  conducting  plates  of  brass,  thus  securing 
both  a  reduction  of  the  transverse  resistance  and  a  large 
amount  of  surface-exposure  to  light.  Thus  a  cell,  whose 
resistance  in  the  dark  was  300  ohms,  when  exposed  to 
sunlight  had  a  resistance  of  but  I  50  ohms.  This  pro- 
perty of  selenium  the  latter  experimenters  have  applied 
in  the  construction  of  the  Photophone,  an  instrument 
which  transmits  sounds  to  a  distance  by  means  of  a 
beam  of  light  reflected  to  a  distant  spot  from  it  Ihfn 
mirror  thrown  into  vibrations  by  the  voice ;  the  beain 
falling,  consequently,  with  varying  intensity  upon  a  re- 
ceiver of  selenium  connected  in  circuit  with  a  small 
battery  and  a  Bell  telephone  (Art.  435)  in  which  the 
Sounds  are  reproduced  by  the  variations  of  the  current. 

Similar  properties  are  possessed,  to  a  smaller  degree, 
by  tellurium.      Carbon  is  also  sensitive  to  light. 

About  the  middle*"  of  the  present  century  Becquerel 
showed    that    when   two    plates  of  silver,  coated    with 


CHAP,  ix.]   ELECTRICITY  AND  MAGNETISM,  359 

freshly  deposited  chloride  of  silver,  are  placed  in  a  cell 
with  water  and  connected  with  a  galvanometer,  a  current 
is  observed  to  pass  when  light  falls  upon  one  of  the  two 
plates,  the  exposed  plate  acting  as  a  negative  pole. 

39O.  Electromagnetic  Theory  of  Light. — Clerk 
Maxwell  proposed  a  theory  of  the  relation  betweeri 
electromagnetic  phenomena  and  the  phenomena  of  light, 
based  upon  the  assumption  that  each  of  these  are  due  to 
certain  modes  of  motion  in  the  all- pervading  "  atJier"  of 
space,  the  phenomena  of  electric  currents  and  magnets 
being  due  to  streams  and  whirls,  or  other  bodily  move- 
ments in  the  substance  of  the  aether,  while  light  is  due 
to  vibrations  to  and  fro  in  it. 

We  have  seen  (Arts.  115,  338,  and  387)  what  evidence  there 
is  for  thinking  that  magnetism  is  a  phenomenon  of  rotation, 
there  being  a  rotation  of  something  around  an  axis  lying  in  the 
direction  of  the  magnetisation.  Such  a  theory  would  explain 
the  rotation  of  the  plane  of  polarisation  of  a  ray  passing  through 
a  magnetic  field.  For  a  ray  of  plane-polarised  light  may  be  con- 
ceived of  as  consisting  of  a  pair  of  (oppositely)  circularly-polarised 
waves,  in  which  the  right-handed  rotation  in  one  ray  is  periodi- 
cally counteracted  by  an  equal  left-handed  rotation  in  the  other 
ray ;  and  if  such  a  motion  were  imparted  to  a  medium  in  .which 
there  were  superposed  a  rotation  (such  as  we  conceive  to  take 
place  in  every  magnetic  field)  about  the  same  direction,  one  of 
these  circularly-polarised  rays  would  be  accelerated  and  the  other 
retarded,  so  that,  when  they  were  again  compounded  into  a 
single  plane-polarised  ray,  this  plane  would  not  coincide  with  the 
original  plane  of  polarisation,  but  would  be  apparently  turned 
round  through  an  angle  proportional  to  the  superposed  rotation. 

It  was  'pointed  out  (Art.  337)  that  an  electric  dis- 
placement produces  a  magnetic  force  at  right  angles  to 
itself;  it  also  produces  (by  the  peculiar  action  known  as 
induction)  an  electric  force  which  is  propagated  at  right 
angles  both  to  the  electric  displacement  and  to  the  mag- 
netic force.  Now  it  is  known  that  in  the  propagation  of 
light  the  actual  displacements  or  vibrations  which  con- 
stitute the  so-called  ray  of  light  are  executed  in  directions 
at  right  angles  to  the  direction  of  propagation.  This 


360 


ELEMENTARY  LESSONS  ON       [CHAP.  ix. 


analogy  is  an  important  point  in  the  theory,  and 
immediately  suggests  the  question  whether  the  respective 
rates  of  propagation  are  the  same.  Now  the  velocity 
of  propagation  of  electromagnetic  induction  is  that 
velocity  "v"  which  was  shown  (Art.  365)  to  represent 
the  ratio  between  the  electrostatic  and  the  electro- 
magnetic units,  and  which  (in  air)  is  believed  to  be 

2-9857  x  io10  centimetres  per  second. 
And  the  velocity  of  light  (in  air)  has  been  repeatedly 
measured   (by   Fizeau,   Cornu,   Michelson,   and  others) 
giving  as  the  approximate  value 

2-9992  x  io10  centimetres  per  second. 
The  close  agreement  of  these  figures  is  at  least  remarkable. 
Amongst  other  mathematical  deductions  from  the  theory  may  be 
mentioned  the  following  :  (i. )  all  true  conductors  of  electricity 
must  be  opaque l  to  light ;  (ii. )  for  transparent  media  the 
specific  inductive  capacity  ought  to  be  equal  to  the  square  ot 
the  index  of  refraction.  Experiments  by  Gordon,  Boltzmann, 
and  others,  show  this  to  be  approximately  true  for  waves  of  very 
great  wave-length.  The  values  are  shown  below.  For  gases 
the  agreement  is  even  closer. 


Flint  Glass      . 
Bisulphide  of  Carbon 
Sulphur  (mean) 
Paraffin  . 

K. 

If. 

3-162 
1-812 

2-32 

2-796 
2-606 
4-024 

1  The  author  of  these  Lessons  has  found  that  in  some  crystalline  bodiej 
which  conduct  electricity  better  in  one  direction  than  in  another,  the  opacity 
to  light  differs  correspondingly.  Coloured  crystals  of  Tourmaline  conduct 
electricity  better  across  the  long  axis  of  the  crystal  than  along  that  axis. 
Such  crystals  are  much  more  opaque  to  light  passing  along  the  axis  than 
to  light  passing  across  it  And,  in  the  case  of  rays  traversing  the  crystal 
across  the  axis,  the  vibrations  across  the  axis  are  more  completely  absorbed 
than  those  parallel  to  the  axis  :  whence  it  follows  that  the  transmitted  light 
will  be  polarized. 

Prof.  H.  Hertz  has  shown  (1888)  that  invisible  electric  undulations  are 
propagated  across  space  just  as  light-waves  are  ;  for  he  haj  been  able  to 
produce  the  phenomena  of  interference  between  two  sets  of  them. 


CHAP,  x,]     ELECTRICITY  AND  MAGNETISM.  361 


CHAPTER  X. 

INDUCTION  CURRENTS  (Magneto-Electricity). 
LESSON  'XXXM\.—  Currents  produced  by  Induction. 


391.  In  1831  Faraday  discovered  that  currents  can 
be  induced  in  a  closed  circuit  by  moving  magnets  near 
it,  or  by  moving  the  circuit  across  the  magnetic  field, 
and  he  followed  up  this  discovery  by   finding  that   a 
current    whose    strength    is    changing    may    induce    a 
secondary  current   in   a   closed  circuit  near  it.      Such 
currents,   whether   produced    by  magnets    or  by   other 
currents,  are  known  as  Induction  Currents.     And 
the  action  of  a  magnet  or  current  in   producing  such 
induced  currents  is  termed  electromagnetic  induc- 
tion. i 

392.  Induction  Currents  produced  by  a  Mag- 
net. —  If  a  coil  of  insulated  wire  be  connected  in  circuit 
with  a  delicate  (long  -coil)  galvanometer,  and  a  magnet 
be  inserted  rapidly  into  the  hollow  of  the  coil  (as  in  Fig. 

l  The  student  must  not  confuse  this  electromagnetic  induction  with  the 
phenomenon  of  the  electrostatic  induction  of  one  charge  of  electricity  by 
another  charge^  as  explained  in  Lesson  III.,  and  which  has  nothing  to  do 
with  currents.  Formerly,  before  the  identity  of  the  electricity  derived  from 
different  sources  was  understood  (Art.  ?i8),  electricity  derived  thus  from  the 
motion  of  magnets  was  termed  magneto-electricity.  For  most  purposes  the 
adjectives  Magneto-electric  and  electro  -magnetic  rre  synonymous.  Th« 
production  of  electricity  from  magnetism,  and  of  magnetism  from  electricity, 
are,  it  is  true,  two  distinct  operations  ;  but  both  are  included  in  the  branch 
of  science  denominated  Eleciroinagnetics. 


ELEMENTARY  LESSONS  ON         [CHAP.  x. 


146),  a  momentary  current  is  observed  to  flow  round 
the  circuit  while  the  magnet  is  being  moved  into  the 
coil.  So  long  as  the  magnet  lies  motionless  in  the  coil 
it  induces  no  currents.  But  if  it  be  rapidly  pulled  out  of 

the  coil  another  momentary 
current  will  be  observed  to 
flow,  and  in  the  opposite  direc- 
tion to  the  former.  The  in- 
duced current  caused  by  in- 
serting the  magnet  is  an 
inverse  current,  or  is  in  the 
opposite  direction  to  that 
which  would  magnetise  the 
magnet  with  its  existing  polar- 
ity. The  induced  current 
caused  by  withdrawing  ihe 
magnet  is  a  direct  current. 

Precisely  the  same  effect  is 
produced  if  the  coil  be  moved 
towards  the  magnet  as  if  the 
magnet  were  moved  toward 
the  coil.  The  more  rapid  the  motion  is,  the  stronger 
are  the  induced  currents. 

393.  Induction  Currents  produced  by  Cur- 
rents.—  Faraday  also  showed  that  the  approach  or 
recession  of  a  current  might  induce  a  current  in  a  closed 
circuit  near  it.  This  may  be  conveniently  shown  as  an 
experiment  by  the  apparatus  of  Fig.  147. 

A  coil  is  joined  up  to  a  sensitive  galvanometer  as 
before.  A  smaller  coil  of  stout  wire  is  connected  to  the 
poles  of  a  battery  (a  single  Bunsen's  cell  in  Fig.  147),  so 
as  to  be  traversed  by  a  current.  On  approaching  or 
inserting  the  smaller  or  "primary"  coil  into  the  larger 
or  "  secondary "  coil,  a  momentary  inverse  current  is 
produced  ;  and  on  removing  it  a  momentary  direct 
current  (/.<?.,  one  which  runs  the  same  way  round  the 
outer  secondary  coil  as  the  primary  current  which 


Fig.  146. 


CHAP,  x.]     ELECTRICITY  AND  MAGNETISM. 


363 


circulates  in  the  inner  coil)  is  observed.     Breaking  the 
batter}'  circuit  while  the  primary  coil  lies  still  within  the 


to 

£ 


secondary  outer  coil  produces  the  same  effect  as  if  the 
primary  coil  were  suddenly  removed  to  an  infinite  dis- 
tance. Making  the  battery  circuit  while  the  primary 


364 


ELEMENTARY  LESSONS  ON        [CHAP.  x. 


coil  lies  within  the  secondary  produces  the  same  effect 
as  plunging  it  suddenly  into  the  coil. 

So  long  as  a  steady  current  traverses  the  primary 
circuit  there  are  no  induced  currents  in  the  secondary 
circuit,  unless  there  is  relative  motion  between  the  two 
circuits  :  but  moving  the  secondary  circuit  towards  the 
primary  has  just  the  same  effect  as  moving  the  primary 
circuit  towards  the  secondary,  and  vice  versa. 

We  may  tabulate  these  results  as  follows  : — 


By 
means 
of 

Momentary  Inverse 
currents  are  induced 
in  the  secondary  circuit 

Momentary  Direct 
currents  are  induced 
in  the  secondary  circuit 

Magnet 

while  approaching. 

while  receding. 

Current 

while  approaching, 
or  beginning, 
or  increasing  in  strength. 

while  receding^ 
or  ending, 
or  decreasing  in  strength. 

394.  Fundamental  Laws  of  Induction. — When 
we  reflect  that  every  circuit  traversed  by  a  current  has  a 
field  of  magnetic  force  of  its  own  in  which  there  are  lines- 
of-force  running  through  the  circuit  (Art.  192),  and  that  a 
coil  of  many  turns  has  a  field  in  which  the  lines-of-force 
are  distributed  almost  identically  as  those  -of  a  magnet 
are,  we  shall  see  that  the  facts  tabulated  in  the  preceding 
paragraph  may  be  summed  up  in  the  following  funda- 
mental laws  : — 

(i.)  A  decrease  in  the  number  of  lines-of-force  •which 
pass  through  a  circuit  produces  a  current  round 
the  circuit  in  the  positive  direction  (t.e.,  produces 
a  "  direct "  current) ;  while  an  increase  in  the 
number  of  lines-of-force  which  pass  through  the 


CHAP,  x.]     ELECTRICITY  AND  MAGNETISM/          365 

circuit  produces  a  current  in  the  negative  direction 
roietrt  the  circuit. 

Here  we  suppose  the  positive  direction  along  Knes-of-force  to 
be  the  direction  along  which  a  free  N.-pole  would  tend  to  move, 
and  positive  direction  round  the  circuit  to  be  the  same  as  the 
direction  in  which  the  hands  of  a  clock  move.  (See  also  p.  275.) 

(ii.)  The  total  induced  electromotive  -force  acting 
round  a  closed  circuit  is  equal  to  the  rate  oj 
decrease  in  the  number  of  lines  -of  -force  which 
pass  through  the  circuit. 

Suppose  at  first  the  number  of  lines-of-force  passing  through 
the  circuit  to  he  NI}  and  that  after  a  very  short  interval  of  time, 
/,  they  are  N2,  then  the  total  in-luced  electi  emotive  -force  E  is 


By  Ohm's  law,  C  =  E  -=-  R,  therefore 
r  _  Ni  —  Na 

"Rl      : 

If  N2  is  greater  than  N1}  and  there  is  an  increase  in  the  number 
of  line?-of-foice,  then  N!  —  N2  will  be  a  negative  quantity,  and 
C  will  have  a  negative  sign,  showing  that  the  current  is  an 
inverse  one. 

A  reference  to  Fig.  1  34  will  make  this  important  law  clearer. 
Suppose  ABCD  to  he  a  wire  chcuit  of  which  the  piece  AB  can 
slide  along  DA  and  CB  towards  S  and  T.  Let  the  vertical 
arrows  represent  vertical  •  lines  of  force  in  a  uniform  magnetic 
field,  and  show  (as  is  the  case  with  the  veitical  components 
of  the  earth's  lines-of-force  in  the  northern  -hemisphere)  the 
diiection  in  which  a  N.  -pointing  pole  would  move  if  fiee.  The 
positive  direction  of  these  lines  of  force  is  theiefore  veitically 
downwards  through  the  circuit.  Now  if  AB  slide  towards  ST 
with  a  uniform  velocity  it  will  cut  a  certain  number  of  lines-of- 
force  every  second,  and  a  certain  number  will  be  added  during 
every  second  of  time  to  the  total  number  passing  through  the 
circuit.  If  Nj  be  the  number  at  the  beginning,  and  N2  that  at 
the  end  of  a  circuit,  Nx  —  N2  will  be  a  negative  quantity,  and 
there  will  be  an  electromotive  -force  round  the  i-ircuit  whose 
diiection  through  the  sliding  piece  is  from  A  towards  B. 

395.  The  following  adaptation  of  Ampere's  rule  to  the  case 
of  induction  may  be  useful  :  Suppose  a  figure  swimming  in  any 
condtulor  to  turn  so  cs  lo  look  altng  the  (positive  direction  of  the) 


366  ELEMENTARY  LESSONS  ON        [CHAP,  x 

lines-of-forcet  then  if  he  and  the  conductor  be  moved  towards  his. 
right  hand  he  will  be  swimming  wilh  the  ciirrenl  induced  by  this 
motion  ;  if  he  be  moved  towards  his  left  hand,  the  current  will 
be  against  him. 

396.  Lena's  Law. —  In  Art.  320  it  was  laid  down  that  a 
circuit  traversed  by  a  current  experiences  a  force  tending  to 
move  it  so  as  to  include  the  greatest  possible  number  of  lines- 
of-force  in  the  embrace  of  the  circuit.  •  But  if  the  number  of 
lines-of-force  be  increased,  during  the  increase  there  will  be  an 
opposing  (or  negative)  electromotive  -  force  set  up,  which  will 
tend  to  stop  the  original  current,  and  therefore  tend  to  stop  the 
motion.  •  If  there  be  no  current  to  begin  with,  the  motion  will 
generate  one,  which  being  in  a  negative  direction  will  tend  to 
diminish  the  number  of  lines-of-force  passing  through  the 
circuit,  and  so  stop  the  motion.  Lenz,  in  1834,  summed  up 
the  matter  by  saying  that  in  all  ca^es  of  electromagnetic  induction 
the  induced  currents  have  such  a  direction  that  their  reaction 
tends  to  stop  the  motion  which  produces  them.  This  is  known 
as  Lenz's  Law. 

397.  Mutual  Induction  of  Two  Circuits. — In 
Art. 3 20  it  was  shown  that  when  two  circuits,  in  which 
currents  of  unit  strength  are  flowing,  are  placed  near 
together,  they  have  a  mutual  potential  whose  value  \ve 
called  M.  This  symbol  M,  upon  investigation,  was 
found  to  represent  the  number  of  lines-of-force  which 
each  circuit  induced  through  the  other  circuit,  or  was 
"  the  number  of  each  other's  lines  -  of-  force  mutually 
intercepted  by  both  circuits  when  each  carries  unit 
current."  This  number  depended  upon  the  form  and 
pobition  of  the  circuits,  and  was  greatest  when  they 
were  brought  as  near  together  as  possible.  Hence 
we  may  regard  this  quantity  M  as  the  "  coefficient 
of  mutual  induction "  of  the  two  circuits ;  and  any 
movement  of  either  circuit  which  alters  the  number 
of  lines-of-force  passing  mutually  through  them,  will 
be  accompanied  by  the  production  of  induced  cur- 
rents  in  each.  It  can  be  shown  mathematically  that, 
in  the  case  of  two  simple  circular  circuits  of  equal  size, 
enclosing  area  S,  the  greatest  number  of  lines-of-force 


CHAP,  X,]     ELECTRICITY  AND  MAGNETISM.  367 

each  can  induce  through  the  other,  when  each  carries 
unit  current,  is  47rS.  which  is  the  maximum  value  of 
M.  If  the  circuits  are  not  simple,  but  have  respectively 
;/*  turns  and  n  turns,  then  the  value  of  M  will  be 
4?rS  x  ;//;/.  when  the  circuits  coincide  with  each  other. 

398.  The  Induction  Coil. — Induced  currents  have 
in  general  enormously  high  electromotive-forces,  and  are 
able  to  spark  across  spaces  that  ordinary  battery  cur- 
rents cannot  possibly  cross.  In  order  to  observe  these 
effects  a  piece  of  apparatus  invented  by  Mason,  and  im- 
proved by  Ruhmkorff,  and  termed  the  Induction  Coil  or 
Inductorium  (Fig.  148),  is  used.  The  induction  coil  con- 
sists of  a  cylindrical  bobbin  having  a  central  iron  core 


M. 


Fig.  148. 

surrounded  by  a  short  inner  or  "  primary  "  coil  of  stout 
wire,  and  by  an  outer  "  secondary >J  coil  consisting  of  many 
thousand  turns  of  very  fine  wire,  very  carefully  insulated 
between  its  different  parts.  The  primary  circuit  is  joined 
to  the  terminals  of  a  few  powerful  Grove's  or  Bunsen's 
cells,  and  in  it  are  also  included  an  interrupter,  and  a 
commutator  or  key.  The  object  of  the  interrupter  js 


368  ELEMENTARY  LESSONS  ON        [CHAP.  x. 

to  make  and  break  the  primary  circuit  in  rapid  suc- 
cession. The  result  of  this  is  at  every  "  make  "  to  induce 
in  the  outer  "  secondary "  circuit  a  momentary  inverse 
current,  and  at  every  "break"  a  powerful  momentary 
direct  current.  The  currents  at  "make"  are  sup- 
pressed, as  explained  below :  the  currents  at  "  break  " 
manifest  themselves  as  a  brilliant  torrent  of  sparks 
between  the  ends  of  the  secondary  wires  when  brought 
near  enough  together.  The  primary  coil  is  made  of 
stout  wire,  that  it  may  carry  strong  currents,  and  producs 
a  powerful  magnetic  field  at  the  centre,  and  is  made  of 
few  turns  to  keep  the  resistance  low,  and  to  avoid  self- 
induction  of  the  primary  current  on  itself.  The  central 
iron  core  is  for  the  purpose  of  increasing,  by  its  great 
coefficient  of  magnetic  induction,  the  number  of  lines- 
of- force  that  pass  through  the  coils :  it  is  usually  made 
of  a  bundle  of  fine  wires  to  avoid  the  induction  currents, 
which  if  it  were  a  solid  bar  would  be  set  circulating  in 
it,  and  which  would  retard  its  rapidity  of  magnetisation 
or  demagnetisation.  The  secondary  coil  is  made  with 
many  turns,  in  order  that  the  coefficient  of  mutual 
induction  may  be  large ;  and  as  the  electromotive-force 
of  the  induced  currents  will  be  thousands  of  volts,  its 
resistance  will  be  immaterial,  and  it  may  be  made  of  the 
thinnest  wire  that  can  conveniently  be  wound.  In  Mr. 
Spottiswoode's  giant  Induction  Coil  (which  yields  a 
spark  of  42 1  inches'  length  in  air,  when  worked  with  30 
Grove's  cells),  the  secondary  coil  contains  280  miles  of 
wire,  wound  in  340,000  turns,  and  has  a  resistance  of 
over  100,000  ohms. 

The  interruptors  of  induction  coils  are  usually  self- 
acting.  That  of  Foucault,  shown  with  the  coil  in  Fig. 
148,  consists  of  an  arm  of  brass  L,  which  dips  a  platinum 
wire  into  a  cup  of  mercury  M,  from  which  it  draws  the 
point  out,  so  breaking  circuit,  in  consequence  of  its 
other  end  being  attracted  toward  the  core  of  the  coil 
whenever  it  is  magnetised  ;  the  arrn  being  drawn  back 


CHAP,  x.]     ELECTRICITY  AND  MAGNETISM.  369 

again  by  a  spring  when,  on  the  breaking  of  the  circuit, 
the  core  ceases  to  be  a  magnet.  A  more  common 
interrupter  on  small  coils  is  a  "  break,"  consisting  of  a 
piece  of  thin  steel  which  makes  contact  with  a  platinum 
point,  and  which  is  drawn  back  by  the  attraction  of  the 
core  on  the  passing  of  a  current ,'  and  so  makes  and 
breaks  circuit  by  vibrating  backwards  and  forwards  just 
as  does  the  hammer  of  an  ordinary  electric  bell. 

Associated  with  the  primary  circuit  of  a  coil  is  usually 
a  small  condenser^  made  of  alternate  layers  of  tinfoil  and 
paraffined  paper,  into  which  the  current  flows  whenever 
circuit  is  broken.  The  object  of  the  condenser  is,  firstly, 
to  make  the  break  of  circuit  more  sudden  by  preventing 
the  spark  of  the  "  extra- current  "  (due  to  self-induction 
in  the  primary  circuit)  (Art.  404)  from  leaping  across 
the  interrupter ;  and,  secondly,  to  store  up  the  electricity 
of  this  self-induced  extra-current  at  break  for  a  brief 
instant,  and  then  discharge  it  back  through  the  primary 
coil  so  as  to  hasten  demagnetisation  and  so  augment 
the  induced  direct  electromotive-force  in  the  secondary 
coil. 

399.  Buhmkorff's    Commutator. —  In    order  to 
cut  off  or  reverse  the  direction  of  the  battery  current  at 
will,  Ruhmkorff  invented  the  commutator  or  current- 
reverser,  shown  in  Fig.  149.     In  this  instrument  the 
battery   poles   are   connected   through  the  ends   of  the 
axis  of  a  small  ivory  or  ebonite  cylinder  to  two  cheeks 
of  brass  V  aad  V,  which  can  be  turned  so  as  to  place 
them  either  way  in  contact  with  two  vertical  springs  B 
ancr  C,  which  are  joined  to  the  ends  of  the  primary  coil. 
Many  other  forms  of  commutator  have  been  devised ; 
one,  much  used  as  a  key  for  telegraphic  signalling,  is 
drawn  in  Fig.  159. 

400.  Luminous  Effects  of  Induction  Sparks.— 
The  induction  coil  furnishes  a  rapid  succession  of  sparks 
with  which  all  the  effects  of  disruptive  discharge  may  be 
studied.     These  sparks  differ  only  in  degree  from  those 


370 


ELEMENTARY  LESSONS  ON       [CHAP.  x. 


furnished  by  friction  machines  .and  by  Lcyden  jars  (see 
Lesson  XXIII.  on  Phenomena  of  Discharge). 


Fig.  149. 

For  studying  discharge  through  glass  vessels  and  tubes 
from  which  the  air  has  been  partially  exhausted,  the 
coil  is  very  useful  Fig.  150  illustrates  one  of  the 
many  beautiful  effects  which  can  be  obtained,  the  spark 
expanding  in  the  rarefied  gas  into  flickering  sheets  of 
light,  exhibiting  striae  and  other  complicated  phenomena. 

4O1.  Currents  Induced  in  Masses  of  Metal. — 
A  magnet  moved  near  a  solid  mass  or  plate  of  metal 
induces  in  it  currents,  which,  in  flowing  through  it  fr«?rn 
one  point  to  another,  have  their  energy  eventually 
frittered  down  into  heat,  and  which,  white  they  last, 
produce  (in  accordance  with  Lenz's  law)  electromagnetic 
forces  tending  to  stop  the  motion.  Several  curious 
instances  of  this  are  known.  Arago  discovered  that 
when  a  disc  of  copper  is  rotated  in  its  own  plane  under 
a  magnetic  needle  the  needle  turns  round  and  follows 
the  disc  :  and  if  a  magnet  is  rotated  beneath  a  balanced 
metal  disc  the  disc  follows  the  magnet.  Attempts  were 
made  to  account  for  these  phenomena  —  known  as 


CHAP,  x.]    ELECTRICITY  AND  MAGNETISM. 


371 


Aragats  rotations — by  supposing  there  to  be  a  sort  of 
magnetism  of  rotation,  until  Faraday  proved  them  to 
be  due  to  induction.  A 
magnetic  needle  set  swing- 
ing on  its  pivot  comes  .to 
rest  sooner  if  a  copper  disc 
lies  beneath  it,  the  induced 
currents  stopping  it.  -If  a 
cube  or  disc  of  good  con- 
ducting metal  be  set  spin- 
ning between  the  poles  of 
such  an  electromagnet  as 
that  drawn  in  Fig.  127, 
arid  the  current  be  suddenly 
turned  on,  the  spinning  metal 
stops  suddenly.  If,  by  sheer 
force,  a  disc  be  kept  spin- 
ning between  the  poles  of 
a  powerful  electromagnet  it 
will  get  hot  in  consequence 
of  the  induced  currents  flow- 
ing through  it.  In  fact, 
any  conductor  nvoved  forc- 
ibly across  the  lines -of- 
force  of  a  magnetic  field 
experiences  a  mechanical 
resistance  due  to  the  in- 
duced cunents  which  op- 
pose its  motion. 

4O2.    Induction  -  cur- 
rents from  Earth's  Mag- 
netism.— It  is  easy  to  ob- 
tain induced  currents  fiom  the  earth's  magnetism.     A 
coil  of  fine  wire  joined  to  a  long-coil  galvanometer,  when 
suddenly  inverted,  cuts  the  lines -of- force  of  the  earth's 
magnetism,  and  is  traversed  arcordingly  by  a  current. 

Faraday,  indeed,  applied  this  method  to  investigate 


Fig.  150. 


372  ELEMENTARY  LESSONS  ON        TCHAP.  x., 

the  direction  and  number  of  lines -of  force.  If  a  small 
wire  coil  be  joined  in  circuit  with  a  long  coil  galvan- 
ometer having  a  heavy  needle,  and  the  little  coil  be  sud- 
denly inverted  while  in  a  magnetic  field,  it  will  cut  all 
the  lines-of-force  that  pass  through  its  own  area,  and 
the  sine  of  half  the  angle  of  the  first  swing  (see  Art. 
204)  will  be  proportional  to  the  number  of  lines  of 
force  cut ;  for  with  a  slow-moving  needle,  the  total  quan- 
tity of  electricity  that  flows  through  the  coils  will  be  the 
integral  whole  of  all  the  separate  quantities  conveyed 
by  the  induced  currents,  strong  or  weak,  which  flow 
round  the  circuit  during  the  rapid  process  of  cutting 
the  lines-of-force  ;  and  the  Itttle  coil  acts  therefore  as  a 
magnetic  proof -plane. 

If  the  circuit  be  moved  parallel  to  itself  across  a  urii- 
form  magnetic  field  there  will  be  no  induction  currents, 
for  just  as  many  lines-of-force  will  be  cut  in  moving 
ahead  in  front  as  are  left  behind.  There  will  be  no  cur- 
rent in  a  wire  moved  parallel  to  itself  along  a  line-of-force  ; 
nor  if  it  lie  along  such  a  line  while  a  current  is  sent 
through  it  will  it  experience  any  mechanical  force. 

403.  Earth    Currents.  —  The    variations    of    the 
earth's  magnetism,  mentioned  in  Lesson  XII.,  alter  the 
number  of  lines-of-force  which  pass  through   the  tele- 
graphic circuits,  and  hence  induce  in  them  disturbances 
which  are  known  as  "  earth  currents."     During  magnetic 
storms  the  earth  currents  on  the  British  lines  of  telegraph 
have  been  known  to  attain  a  strength  of  40  milli -amperes, 
which    is-  stronger    than    the    usual    working    currents. 
Feeble  earth  currents  are  observed  every  day,  and  are 
more  or  less  periodic  in  character. 

404.  Self-induction:  Extra  Currents.— In  Art. 
397  the  induction  of  ohe  circuit  upon  another  was  ex- 
plained, and  was  shown  to  depend  upon  the  number  of 
lines-of-force  due  to  one  circuit  which   passed  through 
the  other,  the  coefficient  of  mutual  induction  M  being 
the  number  of  mutual  lines-of-force  embraced  by  both 


CHAP,  x.l     ELECTRICITY  AND  MAGNETISM.  373 

circuits  when  each  carried  unit  current.  Now,  if  two 
such  circuits  approach  one  another  so  as  actually  to 
coincide,  the  mutual  induction  becomes  a  self-induc- 
tion of  the  circuit  on  itself.  For  every  circuit  there  is  a 
coefficient  of  self-induction^  whose  value  depends  upon  the 
form  of  the  circuit,  and  which  will  be  greater  if  the 
circuit  be  coiled  up  into  many  turns,  so  that  one  loop  of 
the  circuit  can  induce  lines-of-force  through  another  loop 
of  the  same.  Let  L  represent  the  coefficient  of  self-in- 
duction of  one  circuit,  and  L'  that  of  a  second  circuit 
equal  to  the  first.  When  these  two  circuits  coincide  with 
one  another  their  coefficient  of  mutual  induction  (/.£.,  the 
number  of  lines-of-force  running  through  both  circuits, 
each  carrying  unit  current)  M  will  be  equal  to  L  +  L'; 
or,  L  =  ^  M.  Now  for  two  coincident  circuits  having 
n  turns'  each,  and  each  of  area  S  (by  Art.  397), 

M  =  4:rS«2; 

hence  the  coefficient  of  self-induction  for  one  circuit 
of  n  turns  coiled  up  in  ^ne  plane, 

L  =;  4irS«». 

The  existence  of  self-induction  in  a  circuit  is  attested  by 
the  so-called  extra-current,  which  makes  its  appear- 
ance as  a  bright  spark  at  the  moment  of  breaking  circuit. 
Ifxhe  circuit  be  a  simple  one,  and  consist  of  a  straight 
wire  and  a  parallel  return  wire,  there  will  be  little  or  no 
self-induction ;  but  if  the  circuit  be  coiled  up,  especially  if 
it  be  coiled  round  an  iron  bar,  as  in  an  electromagnet, 
then  on  breaking  circuit  there  will  be  a  brilliant  spark,  and 
a  person  holding  the  two  ends  of  the  wires  between  which 
the  circuit  is  broken  may.  receive  a  slight  shock,  owing 
to  the  high  electromotive-force  of  this  self-induced  extra 
current.  The  extra  -  current  due  to  self-induction  on 
"making"  circuit  is  an  inverse  current,  and  gives  no  spark, 
but  It  -prevents  the  battery  current  from  rising  at  once  to 
its  full  value.  The  extra-current  on  breaking  circuit  is 
a  direct  current,  and  therefore  increases -the  strength  of 
the  current  just  at  the  moment  when  it  ceases  altogether. 


374  ELEMENTARY  LESSONS  ON        [CHAP.  \V 

405.  Helmholtz's  Equation — Helmholtz,  who  investi- 
gated mathematically  the  effect  of  self-induction  upon  the  strength 
of  a  current,  deduced  the  following  important  equations  to  ex- 
press the  relation  between  the  self-induction  of  a  circuit  and  the 
time  required  to  establish  the  current  at  full  strength  : — 

The  current  of  self-induction  at  any  moment  vill  be  propor- 
tional to  the  rate  at  which  the  current  is  increasing  in  strength. 
Let  T  represent  a  very  short  interval  of  time,  and  let  the  ciment 
increase  during  that  short  interval  from  C  to  C  +c.  The  actual 
increase  during  the  interval  is  t,  and  the  rate  of  increase  in 

strength  is  ^.     Hence,  if  the  coefficient  of  self-induction  be  L, 

the  electromotive-force  of  self-induction  will  be  -  L-,  and,  if 
the  whole  resistance  of  the  circuit  be  R,  the  strength  of  the 
opposing  extra-current  will  l)e-g-~  during  the  short  interval 

T  ;  and  hence  the  actual  strength  of  curren  flow  ing  in  the 
circuit  during  that  short  interval  instead  of  being  (as  by  Ohm's 
Law  it  would  be  if  the  current  were  steady)  C  =  E  •'-  R,  will  i>e 

r  -  E      L  c 
U  ~   R~R*V 

To  find  out  the  strength  at  which  the  cunent  will  have  arrived 
after  a  time  /  made  up  of  a  number  of  such  small  intenals  added 
together  requires  an  application  of  the  integral  calculus,  which 
at  once  gives  the  following  result  : — • 


(where  e  is  the  base  of  tae  natural  logarithms). 

Put  into  words,  this  expression  amounts  to  saying  that  after 
a  lapse  of  /  seconds  the  self-induction  in  a  circuit  on  making 
contact  lias  the  effect  of  diminishing  the  strength  of  the  current  by 
a  quantit) .  the  logarithm  of  whose  reciprocal  »  inversely  propor- 
tional to  the  coefficient  of  self-induction,  and  directly  proportional 
to  the  rrsisfance  of  the  circuit  and  to  the  time  that  has  elapsed 
since  making  circuit. 

A  very  brief  consideration  will  show  that  in  those  cases  where 
the  circuit  i*  so  arranged  that  the  coefficient  of  self-induction, 

L,  is  small  as  compared  with  the  resistance  R,  the  fraction  £ 

•• 

'v;'ii  have  a  high  value,  and  the  term  (,-j^)  will  vanish  from 
,the  equation  for  all  appreciable  values  of  A 


CHAP.  x.J   ELECTRICITY  AND  MAGNETISM.  375 

Where,  however.  L  is  large  as  compared  with  R,  as  in  long 
ccJs.  long  lines  of  telegraph  cable,  etc..  the  value  of  this  term, 
which  stands  for  the  retardation  due  to  self-induction^  may 
become  considerable. 

406.  Induced   Currents   of  Higher   Orders. — 
Professor  Henry  discovered  that  the   variations   in   the 
strength  of  the  secondary  current  could  induce  tertiary 
currents  in  a  third  closed  circuit,  and  that  variations  in 
the  tertiary  currents  might  induce  currents  of  a  fourth 
order,  and  so  on,      A  single  sudden  primary  current  pro- 
duces therefore  two  secondary  currents  (one  inverse  and 
one  direct),  each  of  these  produces  two  tertiary  currents, 
or  four  tertiary  currents  in  all.      But  where  the  primary 
current  simply  varies  in  strength  in  a  periodic  rise  and 
fall, — as  when  a  musical  note  is  transmitted  by  a  micro- 
phone or  telephone  (Art.  435), —  there  will  be  the  same 
number   of  secondary    and    tertiary    fluctuations    as    of 
primary,  each  separate  induction  involving,  however,  a 
retardation  of  a  quarter  of  the  full  period. 

406  (£/.-).  Transformers. — Of  late  years  a  new  use  has 
been  found  for  induction-coils  for  the  distribxition  of  rapidly 
alternating  currents  (see  Art.  411  d}  for  electiic  lighting.  Such 
induction-coils,  known  as  transformers,  usually  consist  of  a 
core  of  thin  plates  or  wires  of  iron,  interlaced  with  two  sets  of 
copper-wire  coils,  a  primary  consisting  of  many  turns  of  thin 
wire,  to  receive  the  incoming  small  cunenls  at  high  potential, 
and  a  secondary  consisting  of  a  few  turns  of  thick  wire,  to  deliver 
the  large  currents  which  go  out  at  low  potential  to  the  lamps. 
The  number  of  watts  given  out  by  the  secondary  is,  in  a  well- 
constructed  transformer,  equal,  within  a  very  small  percentage 
to  the  number  of  watts  supplied  to  the  piimaiy  coil ;  whilst  the 
volts  of  the  secondary  are  to  the  volts  at  the  primary  in  pio- 
portion  to  the  respective  number  of  turns  in  the  two  coils. 

LESSON  XXXVII. — Magneto-electric  and  Dynamo- 
electric  Generators. 

407.  Faraday's  discovery  of  the  inuuction  of  currents 
in  wires  by  moving  them  across  a  magnetic  field  sug- 
gested the  construction  of  magneto-electric  machines 


376  ELEMENTARY  LESSONS  ON        [CHAP.  x. 

lo  generate  currents  in  ptace  of  voltaic  batteries.  Jh 
the  early  attempts  of  Pixii  (1833),  Saxton,  and  Clarie, 
bobbins  of  insulated  wiie  were  fixed  to  an  axis  and  spun 
rapidly  in  front  of  the  poles  of  strong  steel  magnets. 
But.  since  the  currents  thus  generated  were  alternately 
inverse  and  direct  currents,  a  commutator  (which  rotated 
with  the  coils)  was  fixed  to  the  axis  to  turn  the  successive 
currents  all  into  the  same  direction.  The  little  magneto- 
electric  machines,  still  sold  by  opticians,  are  on  this 
principle.  Holmes  and  Van  Malderen  constuicted  moie 
powerful  machines,  the  latter  getting  a  neaier  approach 
to  a  continuous  cunent  by  combining  around  one  axis 
sixty-four  separate  coils  rotating  between  the  poles  oi 
forty  powerful  magnets. 

In  1856  Siemens  devised  an  improved  armature,  in 
which  the  coils  of  wire  were  wound  lengthways  along 
a  spindle  of  peculiar  form,  thereby  gaining  the  advantage 
of  being  able  to  cut  a  greater  number  of  lines- of -foice 
when  rotated  in  the  powerful  "field"  between  the  poles 
of  a  series  of  adjacent  steel  magnets.  The  next  im- 
provement, due  to  Wilde,  was  the  employment  of  elec- 
tromagnets instead-  of  steel  magnets  for  producing  the 
"field"  in  which  the  armature  re\olved;  these  electro- 
magnets being  excited  by  currents  fuiiiished  by  a  small 
auxiliary  magneto-electric  machine,  also  kept  in  rotation. 

4O8.  Dynamo-electric  Machines. — In  1867  the 
suggestion  was  made  simultaneously,  but  independently, 
by  Siemens  and  by  Wheatstone,  that  a  coil  rotating 
between  the  poles  of  an  electromagnet  might  from  the 
feeble  residual  magnetism  induce  a  small  cm  rent,  which, 
when  transmitted  through  the  coils  of  the  electromagnet, 
might  exalt  its  magnetism,  and  so  prepare  it  to  induce 
still  stronger  currents.  Magneto-electric  machines  con- 
structed on  this  principle,  the  coils  of  their  field-magnets 
being  placed  in  circuit  with  the  coils  of  the  lotating 
armature,  so  as  to  be  tra\ersed  by  the  whole  or  by  a 
portion  of  the  induced  currents,  are  known  as  dynamo- 


CHAP,  x.]     ELECTRICITY  AND  MAGNETISM.          377 

electric  machines  or  generators,  to  distinguish  them 
from  the  generators  in  which  permanent  steel  magnets 
are  employed.  In  either  case  the  current  is  due  to 
magneto-electric  induction  ;  and  in  either  case  also  the 
energy  of  the  currents  so  induced  is  derived  from  the 
dynamical  power  of  the  steam-engine  or  other  motor 
which  performs  the  work  of  moving  the  rotating  coils 
of  wire  in  the  magnetic-  field.  Of  the  many  modern 
machines  on  this  principle  the  most  famous  are  those  of 
Siemens,  Gramme,  Brush.  &nd  Edison.  They  differ 
chiefly  in  the  means  adopted  for  obtaining  practical  con- 
tinuity in  the  current.  In  all  of  them  the  electromotive- 
force  generated  is  proportional  to  the  number  of  turns 
of  wire  in  the  rotating  armature,  and  (within  certain 
limits)  to  the  speed  of  revolution.  When  currents  of 
small  electromotive-force,  but  of  considerable  strength, 
are  required,  as  for  electroplating,  the  rotating  armatures 
of  a  generator  must  be  made  with  small  internal  resist- 
ance, and  therefore  of  a  few  turns  of  stout  wire  or  ribbon 
of  sheet  copper.  For  producing  currents  of  high  electro- 
motive-force for  the  purpose  of  electric  lighting,  the 
armature  must  be  driven  very  fast,  and  must  consist  of 
many  turns  of  wire,  or,  where  .very  small  resistance  is 
necessary  (as  in  a  system  of  lamps  arranged  in.  parallel 
arc),  of  rods  of  copper  suitably  connected. 

There  are  several  ways  of  arranging  the  coils  upon  the  rotating 
armature,  and  the  methods  adopted  may  be  classified  as  follows : — 

t.  Drum  Armatures,  in  which  the  coils  are  wound  longitudinally  upon 
the  surface  of  a  cylinder  or  drum.  Examples :  the  Siemens  ( Alteneck) 
and  Edison  machines. 

2.  Ring  Armatures,  in  which  the  coils  are  wound  around  a  ring.    Ex- 

amples :  the  Pacinotfi,  Gramme.  Brush,  Gulcher,  and  Burgin 
machines. 

3.  Pole  Armatures,  in  which  the  coils  are  arranged  radially  with  their 

poles  pointing  outwards.    'Example:  Lontin  machine. 

4.  Disc  Armatures,  having  coils  arranged  in  or  on  a  disc.     Examples : 

Niaudet,  Wallace,  Hopkinson,  and  Gordon.  In  an  early  machine  by 
Faraday  a  simple  copper  disc  rotating  between  the  poles  of  a  magnet 
generated  a  continuous  current. 


37*  ELEMENTARY  LESSONS  ON         [CHAP.  x. 


There  are  aiso  several  ways  of  arranging  the  coils  of 
the  field-magnets,  giving  rise  to  following  classification: — 

i.  Series-Dynamo,  wherein  the  coils  of  the  field-magnets  are  in  series 
with  those  of  the  armature  and  the  external  circuit. 

a.  Shunt- Dynamo,  in  which  the  coils  of  the  held-magnets  form  A  shunt 
rr  shunts  to  the  main  circuit:  and  being  made  of  nuny  turns  of 
thinner  whe,  draw  off  only  a  fracfion  of  thfe  whole  curreut. 

3.  Separately  -excited  Dynamo :  one  in  which  the  currents  u»ed  to  excite 

the  field-magnets  are  derived  from  a  separate  machine. 

4.  Compound-Dynamo :   parti}   excited  by  shunt  coils,  parti)    by  series 

coils. 

All  these  varieties  have  their  appropriate  uses  according  to  ths  conditions 
under  \\  hich  they  are  applied. 

4O9.  Siemens'  Machine.  —  The  d>namo-electiic 
generator,  invented  by  Siemens  and  Von  Hefner  Altencck, 
usually  called  the  Siemens'  machine,  is  shown  in  Fig. 
151.  Upon  a  stout  frame  are  fixed  four  powerful  flat 
electromagnets,  the  right  pair  having  their  N. -poles 
facing  one  another  and  united  by  arched  pieces  or 
cheeks  of  iion.  The  two  S. -poles  of  the  left  pair  are 
similaily  united.  In  the  space  between  the  right  and 
left  cheeks,  which  is,  theiefore,  a  veiy  intense  magnetic 
field,  lies  a  horizontal  axis,  upon  which  rotates  an 
armature  consisting  of  fifty -six  separate  longitudinal 
coils,  each  end  of  eaclr  coil  being  connected  \\ith  a 
copper  bar  forming  one  segment  of  the  collector  or 
commutator  at  the  anterior  end  of  the  axis.  This 
armature  differs  from  the  earlier  simple  longitudinal 
armature  of  Siemens  only  in  the  multiplication  and 
arrangement  of  its  parts,  the  dh  ision  into  so  many  paths 
giving  a  current  which  is  practically  continuous.  The 
collector,  made  up,  as  said,  of  copper  bars  or  segments 
fixed  upon  a  cylinder  of  insulating  material,  may  be 
regarded  as  a  split-tube.  The  current  cannot  pass  from 
one  segment  to  the  next  without  traversing  one  of 
the  fifty-six  coils  of  the  armature  ;  and,  as  the  end  of 
one  coil  and  the  beginning  of  the  next  are  both  con- 
nected to  the  same  commutator  bar,  there  is  a  continuous 
communication  round  the  whole  armature. .  Against  the 


CHAP,  x.]     ELECTRICITY  AND  MAGNETISM.          379 

commutator  press  a  pair  of  metallic  brushes  or  springs, 
as  contact  pieces,  which  touch  opposite  sides  at  points 


Fig.  151. 


above  and  below,  and  so  lead  away  into  the  circuit  the 
current  generated  in  the  coils  of  the  rotating  armature. 
Suppose  the  lines-of-force  in  the  field  to  run  from  right 
to  left,1  and  the  armature  to  rotate  left-handedly,  as  seen 
in  Fig.  151,  then,  by  the,  rule  given  in  Art.  395,  in  all 

1  Their  direction  is  not  exactly  thus  when  the  generator  is  working,  as 
the  magnetic  force  due  to  the  currents  in  the  coils,  which  is  nearly  horizontal 
in  direction,  changes  the  resultant  magnetic  force  to  an  oblique  direction 
across  the  field.  It  is  for  this  reason  that  the  commutator  "  brushes  "  have 
to  be  displaced  with  a  certain  angular  "  lead."  A  similar  displacement  of 
the  brushes  occurs  in  the  Gramme  and  all  other  dynamo-electric  generators, 
the  degree  of  displacement  to  get  maximum  strength  of  current  varying  with 
the  resistances  in  the  external  circuit  and-w'rh  the  wprfc  doncbythe  current' 


380  ELEMENTARY  LESSONS  ON        [CHAP.  x. 

the  separate  wires  of  the  coils,  moving  upwards  on  the 
right,  there  will  be  currents  induced  in  a  direction  from 
the  back  toward  the  front.  In  all  the  separate  wires  of 
the  coils  moving,  downwards  on  the  left  of  the  axis,  the 
induced  currents  will  be  in  a  direction  from  the  front 
toward  the  back.  Hence,  if  the  coils  are  joined  as 
described  to  the  commutator  bars  all  the  currents  thus 
generated  in  one  half  of  the  coils  will  be  flowing  into 
the  external  circuit  at  one  of  the  commutator  brushes ; 
and  all  the  reverse  currents  of  the  other  half  of  the  coils 
will  be  flowing  out  of  the  other  brush.  The  terminal 
screws  connected  by  wires  to  the  commutator  brushes 
correspond  to  the  +  and  —  poles  of  a  galvanic  battery, 
the  coils  of  the  field -magnets  being  included  in  the 
external  circuit. 

41O.  Gramme's  Machine.. — In  1864  Pacinotti  in- 
vented a  magneto-electric  machine,  its  armature  being  a 
toothed  ring  of  iron  with  coils  wound  between  the  pro- 
jections. In  1870  Gramme  invented  a  dynamo-electric 
machine  having  a  ring  armature  differing  only  in  being 
completely  overwound  with  coils  of  insulated  copper 
wires.  The  principle  of  this  generator  is  shown  in 
diagram  in  Fig.  152.  The  ring  itself,  made  of  a  bundle 
of  annealed  iron  wires,  is  wound  in  separate  sections, 
the  ends  of  each  coil  being  joined  to  strips  of  copper 
which  are  insulated  from  each  other,,  and  fixed  sym- 
metrically as  a  commutator  around  the  axis,  like  a  split 
tube.  Their  actual  arrangement  is  shown  again  in  Fig. 
153.  The  coils  of  the  separate  sections  of  the  ring  are 
connected  together  in  series,  each  strip  of  the  commu- 
tator being  united  to  one  end  of  each  of  two  adjacent 
coils.  Against  the  split -tube  collector  press  metallic 
brushes  to  receive  the  current.  When  this  ring  is  rotated 
the  action  is  as  follows  : — Suppose  (in  Fig.  i  52)  the  ring 
to  rotate  in  the  opposite  direction  to  the  hands  of  a  clock 
in  the  magnetic  field  between  the  N  and  S-poles  of  a 
magnet  (or  electro-magnet),  and  that  the  positive  direc- 


CHAP,  x.j     ELECTRICITY  AND  MAGNETISM.          381 

tion  of  the  lines  of  force  is  from  N  to  S.  As  a  matter 
of  fact  the  lines  will  not  be  straight  across  from  N  to  S, 
because  the  greater  part  of  them  will  pass  into  the  ring 
near  N  and  traverse  the  iron  of  the  ring  to  near  S,  where 
they  emerge  ;  the  space  within  the  ring  being  almost 
entirely  destitute  of  them.  Consider  one  single  coil  of 
the  wire  wrapped  round  the  ring  at  E"  which  is  ascending 


Fig.  152. 

toward  S  ;  the  greatest  number  of  lines-of-force  will  pass 
through  its  plane  when  it  lies  near  E",  at  right  angles  to 
the  line  NS.  As  it  rises  toward  S  and  conies  to  E  the 
number  of  lines-of-force  that  traverse  it  will  be  steadily 
diminishing,  and  will  reach  zero  when  it  comes  close  to 
S  and  lies  in  the  line  NS,  edgeways  to  the  lines-of-force. 
As  it  moves  on  toward  E'  it  will  again  enclose  lines-of- 
force.  \\hich  will,  however,  pass  in  the  negative  direction 
through  its  plane,  and  at  E'  the  number  of  such  negatn  e 
lines-of-force  becomes  a  maximum.  Hence,  through  all 
its  journey  from  E"  to  E'  the  number  of  (positive)  lines- 
of-force  embraced  by  a  strand  of  the  coils  has  been 
diminishing  ;  during  its  journey  round  the  other  half  from 
E'  to  E"  again,  the  number  will  be  increasing.  There- 
fore, by  the  rule  given  in  Art.  395,  in  all  the  coils  moving 
round  the  upper _half  of  the  ring:  ^/w/Lcurrents  are  being 


ELEMENTARY  LESSONS  ON       [CHAP.  x. 


generated,  while  in  the  cons  of  the  lower  han  of  the  ring 
inverse  currents  are  being  generated.  Hence  there  is  a 
constant  tendency  for  electricity  to  flow  from  the  left  side 
at  E'  both  ways  round  towards  the  right  side  at  E",  and 
E"  will  be  at  a  higher  potential  than  E'.  A  continuous 


Fig.  153- 

current  will  therefore  be  generated  in  an  external  wire, 
making  contact  at  F  and  F  by  means  of  brushes,  for  as 
each  successive  coil  moves  up  towards  the  brushes  the 
induced  current  in  it  increases  in  strength,  because  the 
coils  on  each  side  of  this  position  are  sending  their 
induced  currents  also  toward  that  point.  Fig.  153  shows 
ithe  little  Gramme  machine,  21  inches  high,  suitable  foci 


CHAP,  x.]     ELECTRICITY  AND  MAGNETISM.          383 

producing  an  electric  arc  light  when  driven  by  a  i\ 
horse-power  engine.  Above  and  below  are  opposite 
pairs  of  powerful  electro-magnets,  whose  iron  pole-pieces 
project  forwards  and  almost  embrace  the  central  ring- 
armature,  which,  with  the  commutator,  is  fixed  10  the 
horizontal  spindle. 

411.  (a)  Brush's  Machine. — In  Brush's  dynamo-electric 
generator,  a  ring-armature  is  also  used,  identical  in  form  with 
that  invented  by  Pacinotti,  the  iron  ring  being  enlarged  with 
protruding  cheeks,  with  spaces  between,  in  which  the  coils  are 
wound,  the  coils  themselves  being  also  somewhat  differently 
joined,  each  coil  being  united  with  that  diametrically  opposite 
to  it,  and  having  for  the  pair  a  commutator  consisting  of  a  collar 
slit  into  two  parts.  For  each  pair  of  coils  there  is  a  similar 
collar,  the  separate  collars  being  grouped  together  and  com- 
municating to  two  or  more  pairs  of  brushes  that  rub  against  them 
the  currents  which  they  collect  in  rotating.  The  electromotive- 
force  of  these  machines  is  very  high,  hence  they  are  able  to 
drive  a  current  through  a  long  row  of  arc  lamps  connected  in 
one  series.  The  largest  Brush  machines  capable  of  maintaining 
65  arc  lights  have  an  electromotive-force  exceeding  3000  volts. 
In  Giilcher's  and  Schuckert's  machines  the  ring-armature  takes 
the  form  of  a  flattened  disk..  In  Crompton's  dynamo  the 
armature  is  wouud  on  a  hollow  cylindiical  core  built  up  of  flat 
thin  iron  rings. 

Siemens  and  others  have  deviled  another  class  of  dynamo- 
electric  machines,  differing  entirely  from  any  of  the  preceding, 
in  which  a  coil  or  other  movable  conductor  slides  round  one 
pole  of  a  magnet  and  cuts  the  lines  of  force  in  a  continuous 
manner  without  any  reversals  in  the  direction  of  the  induced 
currents.  Such  machines,  sometimes  called  "  uni-polar " 
machines,  have,  however,  very  low  electromotive-force. 

411.  (b]  Edison's  Machine. — Some  very  large  dynamo- 
I'lcctric  generators  have  been  constructed  by  Edison  for  his 
system  of  electric  lighting.  This  machine  (as  shown  in  Fig. 
154)  is  built  upon  the  same  bed-plate  as  the  steam  engine  (of- 
1 2O  H-P)  which  drives  it,  and  is  called  by  its  designer  the 
iteam-dynamo.  The  field-magnets  are  placed  horizontally,  and 
consist  of  1 2  cylindrical  iron  bars  overwound  with  wire,  united  to 
solid-iron  pole-pieces  weighing  many  tons.  Between  the  upper 
and  lower  pole-pieces  rotates  the  armature,  which  is  a  modifica- 
tion of  the  drum-armature  of  Siemens,  and  is  made  up  of  9$ 


384  ELEMENTARY  LESSONS  ON        [CHAP.  x. 


CHAP,  x.]   ELECTRICITY  AND  MAGNETISM.  385 

long  rods  of  copper  connected  by  copper  discs  at  the  ends  instead 
of  coils  of  wire.  The  commutator  or  collector  consists  of  49 
parallel  bars  of  copper,  like  the  split-tube  commutator  of  the 
other  machines.  The  circuit  of  the  armature  runs  from  one  bar 
of  the  commutator  along  one  of  the  copper  rods  into  a  coppei 
disc  at  the  far  end,  crosses  by  this  disc  to  the  opposite  rod, 
along  which  it  comes  back  to  the  front  end  to  another  copper 
disc  connected  to  the  next  bar  of  the  commutator,  and  so  on  all 
round.  This  arrangement  greatly  reduces  the  wasteful  resistance 
of  the  armature,  and  adds  to  the  efficiency  of  the  machine.  The 
interior  of  the  armature  is  made  up  of  thin  discs  of  iron  strung 
upon  the  axis  to  intensify  the  magnetic  action  While  avoiding 
the  currents  which  would  be  generated  wastefully  (see  Art.  401) 
in  the  mass  of  the  metal  were  the  iron  core  solid.  There  are 
also  5  pairs  of  brushes  at  the  commutator  to  diminish  sparking. 
This  machine  has  .a  very  high  efficiency,  and  turns  90  per  cent 
of  the  mechanical  power  into  electrical  power.  It  is  capable  of 
maintaining  1300  of  Edison's  incandescent  lamps  (Art.  374) 
alight  at  one  time.  When  driven  at  300  revolutions  per  minute 
the  current  generated  is  about  900  amoeres,  and  the  electio- 
motive-force  105  volts. 

411.  (c)  Theory  of  Continuous- Current  Dynamo.  — The 
electromotive -force  of  a  dynamo  depends  (/')  on  the  number 
of  magnetic  lines  N  which  the  field-magnet  forces  through  the 
armature  core,  passing  into  it  from  the  north-pole  of  the  field- 
magnet  on  one  side,  and  out  of  it  into  the  south-pole  of  the 
field-magnet  on  the  other ;  (ti)  on  the  number  of  conducting 
wires  or  bars  wound  upon  the  armature  ;  (Hi)  on  the  speed  of 
rotation.  If  we  use  the  symbol  C  for  the  number  of  armature 
conductors  counted  all  round  the  periphery,  and  n  for  the 
number  of  revolutions  per  second,  then  the  electromotive -force 
of  the  dynamo  (in  absolute  units)  will  be  given  by  the  rule 

E  =  «CN ; 

but  since  one  volt  is  taken  as  io8  absolute  C.G.S.  units  (see 
Art.  323),  the  electromotive-force  as  expressed  in  volts  will  be 

E  (volts)  =  wCN  -f-  io8. 

The  number  XM  of  magnetic  lines  through  the  armature  can  be 
calculated  by  the  rule  for  the  magnetic  circuit,  given  on  p.  297, 
proper  allowance  being  made  for  inevitable  leakage  of  some  of 
the  magnetic  lines. 

All  and  any  of  the  continuous-current  magneto-electric  and 
dynamo-electric  machines  can  be  used  as  electromotors,  the 


386  ELEMENTARY  LESSONS  ON        [CHAP.  x. 


armature  rotating  and  exerting  power  when  ?,  current  from  an 
independent  source  is  led  into  the  machine. 

411.  (d)  Alternate -Current  Machines. — In  some  dynamo- 
electric  machines  the  alternately-directed  currents  generated  by 
the  successive  approach  and  recession  of  the  coils  to  and  from 
the  fixed  magnet-poles  are  never  commuted,  but  pass  direct  to 
the  circuit.  In  a  typical  machine  of  this  class  invented  by 
Wilde,  the  armature  consists  of  a  series  of  bobbins  arranged 
upon  the  periphery  of  a  disk  which  rotates  between  two  sets  of 
fixed  electromagnets  arranged  upon  circular  frames,  and  pre- 
senting N  and  S- poles  alternately  inward.  The  alternate- 
current  machine  of  Siemens  is  similar  in  design.  Such 
machines  cannot  excite  their  own  field -magnets  with  a  constant 
polarity,  and  require  a  small  auxiliary  direct -current  dynamo  to 
excite  their  magnets.  In  another  machine,  devised  by  De 
Meritens,  a  ring  -  armature,  resembling  those  of  Pacinotti  and 
Brush,  moves  in  front'  of  permanent  steel  magnets.  In  this 
machine  the  current  induced  in  the  circuit  in  one  direction 
while  the  Coils  approach  one  set  of  poles  is  immediately  followed 
by  a  current  in  the  other  direction  as  the  coils  recede  from  this 
set  of  poles  and  approach  the  set  of  poles  of  contrary  sign. 
Alternate-current  machines  have  also  been  devised  by  Lontin, 
Gramme,  and  others,  for  use  in  particular  systems  of  electric 
lighting;  as,  for  example,  the  Jablochkoff  candle  (Art.  374). 
In  Lontin's  machine,  as  in  the  more  recent  and  much  larger 
disk- dynamo  of  Gordon,  the  field-magnet  coils  rotate  between 
two  great  rings  of  fixed  coils  in  which  the  currents  are  in- 
duced. A  recent  form  of  alternate-current  machine,  designed 
by  Ferranti,  differs  from  the  machines  of  Wilde  and  Siemens  in 
the  substitution  of  copper  strips  wound  in  zig-zag,  for  the  set 
of  rotating  bobbins  in  the  armature.  In  Mordey's  alternator 
the  field-magnet  which  rotates  presents  two  crowns  of  opposing 
poles  on  either  side  of  a  stationary  armature. 

411.  («}  Compound -Wound  Machines. — The  field-mag- 
nets of  a  dynamo- electric  machine  are  sometimes  wound  with 
two  sets  of  coils,  so  that  it  can  be  used  as  a  combined  shunt- 
and-series  machine  (see  Art.  408).  Such  machines,  when  run 
at  a  certain  "critical"  speed,  may  be  made  to  yield  their 
current,  at  a  constant  electromotive- force  whatever  the  resistances 
in  circuit. 


CHAP.  xij   ELECTRICITY  AND  MAGNETISM.  387 


CHAPTER    XI. 

ELECTRO-CHEMISTRY. 
LESSON  XXXVIII. — Electrolysis  and  Electrometallurgy. 

412.  In  Lessons  XIV.  and  XVIII.  it  was  explained 
that    a   definite   amount    of  chemical    action   in    a  cell 
evolves   a  current  and  transfers    a  certain  quantity  of 
electricity  through   the  circuit,   and   that,  conversely,  a 
definite  quantity  of  electricity,  in   passing   through  an 
electrolytic  cell,  will  perform  there  a  definite  amount  of 
chemical  work.     The  relation  between  the  current  and 
the  chemical   work  performed  by  it  is  laid  down  in  the 
following  paragraphs. 

413.  Electromotive  -  force    of    Polarisation. — 
Whenever  an  electrolyte   is  decomposed  by  a  current, 
the   resolved    ions    have    a    tendency    to    reunite,    that 
tendency  being  commonly   termed  "  chemical  affinity." 
Thus,  when  zinc   sulphate  (Zn  SO4)  is  split  up  into  Zn 
and  SO4  the  zinc  tends  to  dissolve  again  into  the  solution 
by  reason  of  its  "  affinity  "  for  oxygen  and  for  sulphuric 
acid.     But  zinc  dissolving  into  sulphuric  acid  sets  up  an 
electromotive-force  of  definite  amount ;    and  to  tear  the 
zinc  away  from  the  sulphuric  acid  requires  an  -electro- 
motive-force at  least  as  great  as  this,  and  in  an  opposite 
direction   to    it.     So,  again,   when   acidulated   water  is 
decomposed   in   a   voltameter,  the  separated'  hydrogen 


388  ELEMENTARY  LESSONS  ON       [CHAP.  xi. 

and  oxygen  tend  to  reunite  and  set  up  an  opposing 
electromotive -force  of  no  less  than  1*47  volts.  This 
opposing  electromotive-force,  which  is  in  fact  the  measure 
of  their  "  chemical  affinity,"  is  termed  the  electromotive- 
force  of  polarisation.  It  can  be  observed  in  any  water- 
voltameter  (Art.  208)  by  simply  disconnecting  the 
wires  from  the  battery  and  joining  them  to  a  galvan- 
ometer, when  a  current  will  be  observed  flowing  back 
through  the  voltameter  from  the  hydrogen  electrode 
toward ,  the  oxygen  electrode.  The  polarisation  in  a 
voltaic  cell  (Art.  163)  produces  an  opposing  electro- 
motive-force in  a  perfectly  similar  way. 

Now,  since  the  affinity  of  hydrogen  for  oxygen  is 
represented  by  an  electromotive-force  of  1*47  volts,  it  is 
clear  that  no  cell  or  battery  can  decompose  water  unless 
it  has  an  electromotive -force  at  least  of  1*47  volts. 
With  every  electrolyte  there  is  a  similar  minimum 
electromotive-force  necessary  to  produce  complete^  con- 
tinuous decomposition. 

414.  Theory  of  Electrolysis. — Suppose  a  current 
to  convey  a  quantity  of  electricity  Q  through  a  circuit 
in  which  there  is  an  opposing  electromotive -force  E : 
the  work  done  in  moving  Q  units  of  electricity  against 
this  electromotive-force  will  be  equal  to  E  x  Q.  (If  E 
and  Q  are  expressed  in  "absolute"  C.G.S.  units,  E-Q 
will  be  in  ergs.)  The  total  energy  of  the  current, '  as 
available  for  producing  heat  or  mechanical  motion,  will 
be  diminished  by  this  quantity,  which  represents  the 
work  done  against  the  electromotive-force  in  question. 

But  we  can  arrive  in  another  way  at  an  expression 
for  this  same  quantity  of  work.  For  the  quantity  of 
electricity  in  passing  through  the  cell  will  deposit  a 
certain  amount  of  metal :  this  amount  of  metal  could  be 
burned,  or  dissolved  again  in  acid,  giving  up  its  potential 
energy  as  heat,  and,  the  mechanical  equivalent  of  heat 
being  known,  the  equivalent  quantity  of  work  can  be 
calcuIatedT  Q  units  of  electricity  will  cause  the  depo- 


CHAP,  xi.]   ELECTRICITY  AND  MAGNETISM.  389 

sition  of  Qz  grammes  of  an  ion  whose  absolute  electro- 
chemical equivalent  is  z.  [For  example,  z  for  hydrogen  is 
•00010352  gramme,  being  ten  times  the  amount  (see  table 
in  Art.  212)  deposited  by  one  coulomb,  for  the  coulomb 
is  rV  of  the  absolute  C.G.S.  unit  of  quantity.]  If  H 
represent  the  number  of  heat  units  evolved  by  one 
gramme  of  the  substance,  when  it  enters  into  the  com- 
bination in  question,  then  Q-srH  represents  the  value  (in 
heat  units)  of  the  chemical  work  done  by  the  flow  of  the 
Q  units ;  and  this  value  can  immediately  be  translated 
into  ergs  of  work  by  multiplying  by  Joule's  equivalent  J 
(  =  42  x  io6).  [See  Table  on  page  400.] 
We  have  therefore  the  following  equality  : — 
EQ  =  QsHJ  ;  whence  it  follows  that 

E  =  zH]  ;  or,  in  words,  the  electromotive- 
force  of  any  chemical  reaction  is  equal  to  the  product  of 
the  electro-chemical  equivalent  of  the  separated  ion  into 
its  heat  of  combination,  expressed  in  dynamical  units. 

V 

EXAMPLES.— (I)  Electromotive -force  of  Hydrogen  tending  to 
unite  with  Oxygen.  For  Hydrogen  2  =  -00010352 ;  H 
(heat  of  combination  of  one  gramme)  =  34,000  gramme- 
degree-units  ;  J  =  42  x  io6. 

•00010352  x  34,000  x  42  x  io6=  1-47  x  io8  "absolute" 
units  of  electromotive-force,  or  =  I '47  -volts. 

(2)  Electromotive-force  of  Zinc  dissolving  into  Sulphuric  Acid. 

z  =  '003364 ;  H  =  1670  (according  to  Julius  Thomsen) ; 
J  =  42  x  io6. 

•003364  x  1670  x  42  x  io6  =  2-359  x  io8. 
or  =  2-359  volts. 

(3)  Electromotive-force  ^Copper  dissolving  into  Sulphuric  Acut. 

z  =  -003261  ;  H  =  909-5  ;  J  =  42  x  io« 
•003261  x  909-5  x  42  x  io8  =  1-252  x  10°. 
or  =  i  -252  volts. 

(4)  Electronutive-fcrctofaT>^0!*V&>    Here  rinc  is  dissolved 

at  one  pole  to  form  zinc  sulphate,  the  chemical  actipu  setting 
up  a  +  electromotive-force,  while  at  the  other  pole  copper 
is  deposited  by  the  current  out  of  a  solution  of  copper 
gulphate,  thereby  setting  up  an  opposing  (or  - 


390 


ELEMENTARY  LESSONS  ON      [CHAP.  xi. 


motive  -  force.  That  due  to  zinc  is  shown  above  to  be 
+  2 -3  59  -volts,  that  to  deposited  copper  to  be  -  1-242. 
Hence  the  net  electromotive-force  of  the  ceil  is  (neglecting 
the  slight  electromotive  -  force  where  the'  two  solutions 
touch)  2-359  -  1*242  =  1-117  volts.  This  is  nearly  what 
is  found  (Art.  170)  in  practice  to  be  the  case.  It  is  less 
than  will  suffice  to  electrolyse  water,  though  two  Daniell's 
cells  in  series  electrolyse  water  easily. 

415.  .Secondary  Batteries :  Storage  of  Electric  Currents. 
. — A  voltameter,  or  series  of  voltameters,  whose  electrodes  are 
thus  charged  respectively  with  hy- 
drogen and  oxygen,  will  serve  as 
secondary  latteries,  in  which  the 
energy  of  a  current  may  be  stored  up 
(as  chemical  work)  and  again  given 
out.  Ritter,  who  in  1803  con- 
structed a  secondary  pile,  used  elec- 
trodes of  platinum.  Gaston  Plante", 
in  1860,  devised  a  secondary  cell 
consisting  of  two  pieces  of  sheet 
lead  rolled  up  (without  actual  con- 
tact) as  electrodes,  dipping  into 
dilute  sulphuric  acid,  as  in  Fig. 
155  ;  the  lead  becoming  with  re- 
peated charges  in  alternate  directions 
coated  with  a  semi -porous  film  of 
brown  dioxide  of  lead  on  the.  anode 
plate,  and  on  the  kathode  plate 
assuming  a  spongy  metallic  state 
presenting  a  large  amount  of  surface 
of  high  chemical  activity.  When 
such  a  battery,  or  accumulator  of 
currents,  is  charged  by  connecting  it 
with  a  dynamo- electric  machine  or 
other  powerful  generator  of  currents, 
the  anode  plate  becomes  peroxidise"d, 
while  the  kathode  plate  is  deoxidised  by  the  hydrogen  that 
is  liberated.  The  plates  may  remain  for  many  days  in  this 
condition,  and  will  furnish  a  current  until  the  two  lead  surfaces 
are  reduced  to  a  chemically  inactive  state.  The  electro- 
motive-force of  such  cells  is  about  2'O  volts  during  discharge. 
Plante  has  ingeniously  arranged  batteries  of  such  cells  so  that 
they  can  be  charged  in  parallel  arc,  and  discharged  in  series, 


Fig.  155- 


CHAP.  xr.J  ELECTRICITY  AND  MAGNETISM. 


391 


giving  (for  a  short  time)  currents  of  extraordinary  strength. 
Faure,  in  1 88 1,  improved  the  Plante  accumulator  by  giving  the 
two  lead  plates  a  preliminary  coating  of  red-lead  (or  minium). 
When  a  current  is  passed  through  the  cell  to  charge  it,  the  red- 
lead  is  peroxidised  at  the  anode,  and  reduced, — first  to  a  con- 
dition of  lower  oxide,  then  to  the  spongy  metallic  state, — at  the 
kathode,  and  thus  a  greater  thickness  of  the  working  substance 
is  provided,  and  takes  far  less  time  to  form  than  is  the  case  in 
Plante's  cells.  For  electric  lighting,  Faure's  cells  are  made  up 


Fig.  156. 

with  flat  plates  in  the  form  shown  in  Fig.  156.  In  Sellon's 
and  Volckmar's  accumulators  the  minium  is  packed  into  inter- 
stices in  the  lead  plates.  A  secondary  cell  resembles  a  Leyden 
jar  in  that  it  can  be  charged  and  then  discharged.  Its  time- 
rate  of  leakage  is  also  similar.  The  residual  charges  of  Leyden 
jars,  though  small  in  quantity  and  transient  in  their  discharge, 
yet  exactly  resemble  the  polarisation  charges  of  voltameters. 

416  Grove's  Gas  Battery. — Sir  W.  Grove  devised  a  cell 
in  which  platinum  electrodes,  in  contact  respectively  with  hy- 
drogen and  oxygen  gas,  replaced  the  usual  zinc  and  copper  plates. 
Each  of  these  gases  is  partially  occluded  by  the  metal  platinum, 
which,  when  so  treated,  behaves  like  a  different  metal.  In  Fig. 
157  one  form  of  Grove's  Gas  Battery  is  shown,  the  tubes  O 
and  H  containing  the  +  and  -  electrodes,  surrounded  with 
oxygen  and  hydrogen  respectively. 


392 


ELEMENTARY  LESSONS  ON        [CHAP.  xi. 


417.  General  Laws  of  Electrolytic  Action. — In 

addition  to  Faraday's  quantitative  laws  given  in  Art.  211, 

the  following  are 
important  : — 

(<r.)  Every 
electrolyte  is  de- 
composed into 
two  portions,  an 
anion  ami  a  ka- 
tion,  whicli  may 
be  themselves 
either  simple  or 
compound.  In 
the  case  of  simple 
binary  c  om- 
pounds,  such  as 
fused  salt  (Na 
Cl),  the  ions  are 
simple  elements. 
In  other  cases 
the  products  are 
often  complicat- 
ed by  secondary 
actions.  It  is 
even  possible  to 
deposit  an  alloy 
of  two  metals — 
bras1:  for  example 
— from  a  mix- 
ture of  the  cya- 
nides of  zinc  and 

^«-  J57-  of  copper. 

In  binary  compounds  and  most  metallic  solutions, 

the  metal  is  deposited  by  the  current  where  it  leaves  the 

cell,  at  the  kathode. 

(c.)  Aqueous  solutions  of  salts  of  the  metals  of  the 

alkalies  and  alkaline  earths  deposit  no  metal,  but  evolve 


CHAP,  xi.]    ELECTRICITY  AND  MAGNETISM.  393 

hydrogen  owing  to  secondary  action  of  the  metal  upon 
the  water.  From  strong  solutions  of  caustic  potash  and 
soda  Davy  succeeded  in  obtaining  metallic  sodium  and 
potassium,  which  were  before  unknown.  If  electrodes  of 
mercury  are  employed,  an  amalgam  of  either  of  these 
metals  is  readily  obtained  at  the  kathode.  The  so- 
called  rtWMttWw'jwwiamalgam  is  obtained  by  electrolysing  a 
warm,  strong  solution  of  salammoniac  between  mercury 
electrodes. 

(d:}  ^  Substances  can  be  arranged  in  a  definite  series 
according  to  their  electrolytic  behaviour ;  each  substance 
on  the  list  behaving  as  a  kathion  (or  being  "  electroposi- 
tive ")  when  electrolysed  from  its  compound  with-  any 
other  on  the  list  In  such  a  series  the  oxidisable  metals/ 
potassium,  sodium,  zinc,  etc.,  head  the  list ;  after  which 
come  the  less  oxidisable  or  "electronegative"  metals  J  then 
carbon,  oxygen,  phosphorus,  iodine,  chlorine,  sulphur, 
and  lastly  ozone. 

(<?.)  From  a  solution  of  mixed  metallic  salts  the  least 
electropositive  metal  is  deposited  first,  unless  the  current 
be  very  strong. 

(/.)  The  liberated  ions  appear  only  at  the  elec- 
trodes. 

(,£•.)  For  .each  electrolyte  a  minimum  electromotive- 
force  is  requisite,  without  which  complete  electrolysis 
cannot  be  effected.  (See  Art.  413.) 

(k.)  If  the  current  be  of  less  electromotive-force  than 
the  requisite  minimum,  electrolysis  may  begin,  and  a 
feeble  current  flow  at  first,  but  no  ions  will  be  liberated, 
the  current  being  completely  stopped  as  soon  as  the 
opposing  electromotive-force  of  polarisation  has  risen  to 
equality  with  that  of  the  electrolysing  current. 

(/.)  There  is  no  opposing  electromotive-force  of  polar- 
isation when  electrolysis  is  effected^rom  an  anode  of  the 
same  metal  that  is  being  deposited  at  the  kathode.  The 
feeblest 'cell  will  suffice  to  deposit  copper  from  sulphate  of 
copper  if  the  anode  be  a  copper  plate. 

2  D 


394  ELEMENTARY  LESSONS  ON       ICHAP.  XL 

(/.)  Where  the  ions  are  gases,  pressure  affects  the 
conditions  but  slightly.  Under  300  atmospheres  acid- 
ulated water  is  still  electrolysed  ;  but  in  certain  cases 
a  layer  of  acid  so  dense  as  not  to  conduct  collects  at 
the  anode  and  stops  the  current. 

(k.)  The  chemical  work  done  by  a  current  in  an 
electrolytic  cell  is  proportional  to  the  minimttin  electro- 
motive-force of  polarisation. 

(/.)  Although  the  electromotive-force  of  polarisation 
may  exceed  this  minimum,  the  work  done  by  the  current 
in  overcoming  this  surplus  electromotive-force  will  not 
appear  as  chemical  work,  for  no  more  of  the  ion  will  be 
liberated  ;  but  it  will  appear  as  an  additional  quantity  of 
heat  (or  "local  heat")  developed  in  the  electrolytic  cell. 

(in.)  Ohm's  law  holds  good  for  electrolytic  conduction. 

(;/.)  Amongst  the  secondary  actions  which  may  occur 
the  following  are  the  chief: — (i.)   The  ions  may  them- 
selves decompose  ;  as  SO4  into  SO8  +  O.     (2.)  The  ions 
may  react  on  the  electrodes ;  as  when  acidulated  water 
is  electrolysed  between  zinc  electrodes,  no  oxygen  being 
liberated,  owing  to  the  affinity  of  zinc  for  oxygen.     (3.) 
The  ions  may  be  liberated  in  an  abnormal  state.     Thus 
oxygen  is  frequently  liberated  in  its  allotropic  condition 
as  ozone,  particularly  when  permanganates  are  electro- 
lysed.    The  "  nascent "  hydrogen  liberated  by  the  elec- 
trolysis of  dilute  acid  has  peculiarly  active   chemical 
properties.     So  also  the  metals  are  sometimes  deposited 
abnormally :   copper  in  a  black  pulverulent  film ;   anti- 
mony in  roundish   gray  masses  (from    the    terchloride 
solution)  which  possess  a  curious  explosive  property,  etc 
418.  Hypotheses   of  Grotthuss  and  of  Olaii- 
sius. — A  complete  theory  of  electrolysis  must  explain — 
firstly,  the  transfer  of  electricity,  and,  secondly,  the  transfer 
of  matter,  through  the  liquid  of  the  cell.     The  latter 
point    is   the   one   to    which   most  attention  has  been 
given,  since  the  "  migration  of  the  ions  "  (i.e.  their  trans- 
fer through  the.  liquid)  in  two  opposite  directions,  and 


CHAP,  xi.]    ELECTRICITY  AND  MAGNETISM. 


395 


their   appearance   at    the    electrodes    only,    are    salient 
facts. 

The  hypothesis  put  forward  in  1805  by  Grotthuss 
serves  fairly,  when  stated  in  accordance  with  modern 
terms,  to  explain  these  facts. >•  Grotthuss  supposes  that, 
when  two  metal  plates  at  different  potentials  are  placed 
in  a  cell,  the  first  effect  produced  in  the  liquid  is  that 
the  molecules  of  the  liquid  arrange  themselves  in  in- 
numerable chains,  in  which  every  molecule  has  its 
constituent  atoms  pointing  in  a  certain  direction  ;  the 
atom  of  electropositive  substance  being  attracted  toward 
the  kathode,  and  the  fellow  atom  of  electronegative 
substance  being  attracted  toward  the  anode.  (This 
assumes  the  constituent  atoms  grouped  in  the  molecule 
to  retain  their  individual  electric  properties.)  The 
diagram  of  Fig.  1 58  shows,  in  the  case  of  Hydrochloric 


Fig.  158. 

Acid,  a  row  of  molecules  i,  i,  at  first  distributed  at 
random,  and  secondly  (as  at  2,  2,)  grouped  in  a  chain 
as  described.  The  action  which  Grotthuss  then  sup- 
poses to  take  place  is  that  an  interchange  of  partners 
goes  on  between  the  seoarate  atoms  all  along  the  line,] 


396  ELEMENTARY  LESSONS  ON      [CHAP.  xi. 

each  H  atom  uniting  with  the  Cl  atom  belonging  to  the 
neighbouring  molecule,  a  +  half  molecule  of  hydrogen 
being  liberated  at  the  ka'thode,  and  a  —  half  molecule 
of  chlorine  at  the  anode.  This  action  would  leave  the 
molecules  as  in  3,  3,  and  would,  when  repeated,  result 
in  a  double  migration  of  hydrogen  atoms  in  one  direc- 
tion and  of  chlorine  atoms  in  the  other,  the  free  atoms 
appearing  only  at  the  electrodes,  and  every  atom  so 
liberated  discharging  a  certain  definite  minute  charge  of 
electricity  upon  the  electrode  where  it  was  liberated.1 

Clausius  has  sought  to  bring  the  ideas  cf  Grotthuss 
into  conformity  with  the  modern  kinetic  hypothesis  cf 
the  constitution  of  liquids.  Accordingly,  we  are  to 
suppose  that  in  the  usual  state  cf  a  liquid  the  molecules 
are  always  in  movement,  gliding  about  amongst  one 
another,  and  their  constituent  atoms  are  also  in  move- 
ment, and  are  continually  separating  and  recombining 
into  similar  groups,  their  movements  taking  place  in  all 
possible  directions  throughout  the  liquid.  But  under 
the  influence  of  an  electromotive-force  these  actions  are 
controlled  in  direction^  so  that  when,  in  the  course  cf  tho 
usual  movements,  an  atom  separates  from  a  group  it 
tends  to  move  either  toward  the  anode  or  kathode , 
and  if  the  electromotive  force  in  question  be  powerful 
enough  to  prevent  recombination,  these  atoms  will  be 
permanently  separated,  and  will  accumulate  around  the 
electrodes.  This  theory  has  the  advantage  of  account- 
ing for  a  fact  easily  observed,  that  an  electromotive  force 
less  than  the  minimum  which  is  needed  to  effect  com- 
plete  electrolysis  may  send  a  feeble  current  through  an 

1  Mr.  G.  J.  Stoney  has  lately  reckoned,  from  considerations  founded  on 
the  size  of  atoms  (as  calculated  by  Loochmidt  and  Sir  W.  Thomson),  that 
for  every  chemical  bond  ruptured,  a  charge  of  10 — 2O  of  a  coulomb  i«  trans- 
ferred. [E.  Budde  says  17  X  lo--5  coulomb.]  This  quantity  would  appear 
therefore  to  be  th«  natural  atomic  charge  or  unit.  To  tear  one  atom  of 
hydrogen  from  a  hydrogen  compound  this  amount  of  electricicy  must  be  sent 
through  it.  To  liberate  an  atom  of  zinc,  or  arjy  other  di-valent  metal  from 
its  compound,  Implies  the  transfer  of  twice  this  amount  of  electricity. 


CHAP,  xi.]    ELECTRICITY  AND  MAGNETISM.  397 

electrolyte  for  a  limited  time,  until  the  opposing  electro- 
motive force  has  reached  an  equal  value.  Helmholtz, 
\vho  has  given  the  name  of  electrolytic  convection  to  this 
phenomenon  of  partial  electrolysis,  assumes  that  it  take? 
place  by  the  agency  of  uncombined  atoms  previously 
existing  in  the  liquid.  This  assumption  is  virtually  in- 
cluded in  the  kinetic  hypothesis  of  Clausius. 

419.-  Electrometallurgy. — The  applications  of  elec- 
tro-chemistry to  the  industries  are  threefold.  Firstly^ 
to  the  reduction  of  metals  from  solutions  of  their  ores, 
a  process  too  costly  for  general  application,  but  one 
useful  in  the  accurate  assay  of  certain  ores,  as,  for 
example,  of  copper ;  secondly,  to  the  copying  of  types, 
plaster  casts,  and  metal -work  by  kathode  deposits  of 
metal ;  thirdly,  to  the  covering  of  objects  made  of  baser 
metal  with  a  thin  film,  of  another  metal,  Such  as  gold, 
silver,  or  nickel.  All  these  operations  are"  included 
under  the, general  term  of  electrometallurgy. 

42O.  Electrotyping1. —  In  1836  De  La  Rue  ob- 
served-that  in  a  DanielPs  cell  the  copper  deposited  out 
of  the  solution  upon  the  copper  plate  which  served  as  a 
pole  took  the  exact  impress  of  the  plate,  even  to  the 
scratches  upon  it.  In  1839  Jacobi  in  St.  Petersburg, 
Spencer  in  Liverpool,  and  Jordan  in  London,  independ- 
ently developed,  out  of  this  fact  a  method  of  obtaining, 
by  the  electrolysis  of  copper,  impressions  (in  reversed 
relief)  of  coins,  stereotype  plates,  and  ornaments.  A 
further  improvement,  due  to  Murray,  was  the  employment 
of  moulds  of  plaster  or  wax.  coated  with  a  film  of  filum- 
biro  in  order  to  provide  a  conducting  surface  upon 
which  the  deposit  could  be  made.  Jacobi  gave  to  the 
process  the  name  of  galvano-plastic,  a  term  generally 
abandoned  in  favour  of  the  term  electrotyping  or 
electrotype  process. 

Electrotypes  of  copper  are  easily  made  by'  hanging  a 
suitable  mould  in  cell  containing  a  saturated  solution  of 
sulphate  of  copper,  and  passing  a  current  of  a  battery 


398  ELEMENTARY  LESSONS  ON       [CHAP,  xi, 

through  the  cell,  the  mould  being  the  kathode ;  a  plate 
of  copper  being  employed  as  an  anode,  dissolving  gradu- 
ally into  the  liquid  at  a  rate  exactly  equal  to  the  rate  of 
deposition  at  the  kathode.  This  use  of  a  separate 
battery  is  more  convenient  than  producing  the  electro- 
types in  the  actual  cell  of  a  Daniell's  battery.  The 
process  is  largely  employed  at  the  present  day  to  repro- 
duce repousse"  and  chased  ornament  and  other  works  of 
art  in  facsimile,  and  to  multiply  copies  of  wood  blocks 
for  printing.  Almost  all  the  illustrations  in  this  book, 
for  example,  are  printed  from  electrotype  copies,  and  not 
from  the  original  wood  blocks,  which  would  not  wear  so 
well. 

421.  Electroplating. — In  1801  Wollaston  observed 
that  a  piece  of  silver,  connected  with  a  more  positive 
metal,  became  coated  with  copper  when  put  into  a 
solution  of  copper.  In  1805  Brugnatelli  gilded  two 
silver  medals  by  making  them  the  kathodes  of  a  cell 
containing  a  solution  of  gold.  Messrs.  Elkington,  about 
the  year  1840,  introduced  the  commercial  processes  of 
electroplating.  In  these  processes  a  baser  metal,  such 
as  German  silver  (an  alloy  of  zinc,  copper,  and  nickel) 
is  covered  with  a  thin  film  of  silver  or  gold,  the  solutions 
employed  being,  for  electro-gilding,  the  double  cyanide 
of  gold  and  potassium,  and  for  ejectro- silvering  the 
double  cyanide  of  silver  and  potassium. 

Fig.  159  shows  a  battery  and  a  plating-vat  contain;ng 
the  silver  solution.  From  the  anode  is  hung  a  plate  of 
metallic  silver  which  dissolves  into  the  liquid.  To  the 
kathode  are  suspended  the  spoons,  forks,  or  other 
articles  which  are  to  receive  a  coating  of  silver.  The 
addition  of  a  minute  trace  of  bisulphide  of  carbon  to  the 
solution  causes  the  deposited  metal  to  have  a  bright 
surface.  If  the  current  is  too  strong,  and  the  deposition 
too  rapidj  the  deposited  metal  is  grayish  and  crystalline. 

In  silvering  or  gilding  objects  of  iron  it  is  usual  first 
to  plate  them  with  a  thin  coating  of  copper.  In  gilding 


CHAP,  xi.]   ELECTRICITY  AND  MAGNETISM. 


399 


base  metals,  such  as  pewter,  they,  are  usually  first 
copper-coated.  The  gilding  of  the  insides  of  jugs  and 
cups  is  effected  by  filling  the  jug  or  cup  with  the  gilding 
solution,  and  suspending  in  it  an  anode  of  gold,  the  vessel 
itself  being  connected  to  the  -  pole  of  the  battery. 


Fig.  159. 

Instead  of  a  battery  a  thermo-electric  generator  (Art. 
384),  or  a  dynamo-electric  generator  (Art.  408),  is  now 
frequently  employed. 

i  422.  Metallo-chromy.— In  1826  Nobili  discovered  that  when 
a  solution  of  lead  is  electrolysed  a  film  of  peroxide  of  lead  forms 
upon  the  anode.  If  this  be  a  sheet  of  metal,  —  a  plate  of 
polished  steel,  for  instance, — placed  horizontally  in  the  liquid 
beneath  a  .platinum  wire  as  a  kathode,  the  deposit  takes  place 
in .  symmetrical  rings  of  varying  thickness,  the  thickest  deposit 
being  at  the  centre.  These  -rings,  known  as  Nobili's  rings, 
exhibit  all  the  tints  of  the  rainbow,  owing  to  interference  of 
the  w.aves  of  light^  occurring  in  the  film  causing  rays  of  different 
•wave-length  and  colour  to  be  suppressed  at  different  distances 
from  the  centre  The  colours  form,  in  fact,  in  reversed  order, 
the  "colours  of  thin  plates"  of  Newton's  rings.  According 
to  Wagner  this  production  of  chromatic  effects  by  electrolysing 
a  solution  of  lead  in  caustic  soda,  is  applied  in  Nuremberg  to 
ornament  metallic  toys.  The  author  Of  these  Lessons  has 
kpbserve.d  thaV_when  Nobili's  rings  are  made  in  a  magnetic 


400 


ELEMENTARY  LESSONS  ON      [CHAP.  xi. 


field  they  nre  no  longer  circular,  the  depositing  currents  being 
drawn  aside  in  a  manner  which  could  be  predicted  from  the 
observed  action  of  magnets  on  conductors  carrying  currents. 

422  (bis).  Electro  -  Chemical  Power  of  Metals.  —  The 
following  Table  gives  the  electromotive -force  of  the  different 
metals  as  calculated  by  the  method  of  Art.  414  from  their 
electro  •  chemical  equivalents  (Art.  2 1 2),  and  from  the  heat 
evolved  by  the  combination  with  oxygen  of  a  portion  of  the 
metal  equivalent  electro-chemically  in  amount  to  one  gramme 
of  hydrogen.  The  electromotive  -  forces  (in  vclts)  as  observed 
(in  dilute  sulphuric  acid)  are  added  for  comparison. 


TT     _A    ^f 

E.  M.  F. 

calculated. 

ETVT      TT1 

Substance. 

Heat  of 
Equivalent. 

Relatively 
to  Oxygen. 

Relatively 
to  Zinc. 

.  JV1.  r  . 
observed. 

Potassium      .     . 

69,800 

3'01 

+  1  18 

+.I-I3 

Sodium     .     . 

67,800 

2'9I 

+  '1*09 

Zinc     .... 

42,700 

I-83 

0' 

O' 

Iron     .... 

34.120 

I'55 

-0-28 

Hydrogen      .     . 

34,000 

I'47 

-0-36 

Lead    .... 

25,100 

I'I2 

-071 

-0'54 

Copper     .     .     . 

18,760 

•80 

-    -08 

-  I  -047 

Silver  .... 

9,000 

•'39 

-    "44 

.Platinum  .     .     . 

7,500 

"33 

-    -50 

-  I'53 

Carbon     .     .     . 

2,000 

•09 

-    74 

...- 

Oxygen     .     .     . 

o 

0' 

-    "83 

-.1*5 

(Nitric  Acid)      . 

-  .  6,000 

-  O'26 

-  2*09 

-1-94 

(Black  Oxide  of 
Manganese) 

-   6,  500 

-  O'29 

-  2'12 

-  2-23 

(Peroxide  of  Lead) 

-12,150 

-  O'52 

-2-35 

-  2'52 

(Ozone)    .     .     . 

-  14,800 

-0-63 

-  2-46 

-  2  '64 

(Permanganic 
.  Acid)     .    ,     . 

-  25,070 

-  1*09 

-  2-92 

-3'03 

The  order  in  which  these  metals  are  arranged  is  in  fact  nothing  else  than 
the  order  of  oxidisability  of  the  metals  (in  the  presence  of  dilute  sulphuric 
acid)  ;  for  that  metal  tends  most  to  oxidise  which  can, -by  oxidising,  give  out 
the  most  energy.  It  also  shows  the  order  in  which  the  metals  stand  in  their 
power  to  replace  one  another  (in  a  solution  containing  sulphuric  acid.)  In 
this  order  too,  the  lowest  on  the  list  first,  are  the  metals  deposited  by  an 
electric  current  from  solutions  containing  two  or  more  of  them :  for  that 
metal  comes  down  first  which  requires  the  least  expenditure  of  energy  to 
it  frorn  the  elements  with  wai-,h  ii  was  combined 


CHAP,  xn.l  ELECTRICITY  AND  MAGNETISM.         401 


CHAPTER  XII. 

TELEGRAPHS  AND  TELEPHONES. 
LESSON  XXXIX. — Electric  Telegraphs. 

42&  The  Electric  Telegraph. — It  is  difficult  to  assign  the 
invention  of  the  Telegraph  to  any  particular  inventor.  Lesage 
(Geneva,  1774),  Lomond  (Paris,  1787),  and  Sir  F.  Ronalds 
(London,  1816),  invented  systems  for  transmitting  signals 
through  Wires  by  observing  at  one  end  the  divergence  of  a  pair 
of  pith-balls  when  a  charge  of  electricity  was  sent  into  the  other 
end.  Cavallo  (London,  1795)  transmitted  sparks  from  Leyden 
jars  through  wires  "according  to  a  settled  plan."  Soemmering 
(Munich,  1808)  established  a  telegraph  in  which  the  signals 
were  made  by  the  decomposition  of  water  in  voltameters  ;  and 
the  transmission  of  signals  by  the  chemical  decomposition  of 
substances  was  attempted  by  Coxe,  R.  Smith,  Bain,  and  others. 
Ampere  (Paris,  1821)  suggested  that  a  galvanometer  placed  at 
a  distant  point  of  a  circuit  might  serve  for  the  transmission  of 
signals.  Schilling  and  Weber  (Gottingen,  1833)  employed  the 
deflections  of  a  galvanometer  needle  moving  to  right  or  left  to 
signal  an  alphabetic  code  of  letters  upon  a  single  circuit 
Cooke  and  Wheatstone  (London,  1837)  brought  into  practical 
application  the  first  form  of  their  needle  telegraph.  Henry 
(New  York,  1831)  utilised  the  attraction  of  an  electromagnet 
to  transmit  signals,  the  movement  of  the  armature  producing 
audible  sounds  according  to  a  certain  code.  Morse  (New  York, 
1 83  7)  devised  a  telegraph  in  which  the  attraction  of  an  arma- 
ture by  an  electromagnet  was  made  to  mark  a  dot  or  a  dash 
upon  a  moving  strip  of  paper.  Steinheil  (Munich,  1837) 
discoveied  that  instead  of  a  return- wire  the  earth  might  be  used, 
contact  being  made  to  earth  at  the  two  ends  by  means  of  earth 


402 


ELEMENTARY  LESSONS  ON     [CHAP.  xn. 


plates  (see  Fig.  160)  sunk  in  the  ground.  Gintl  (1853)  and 
Stearns  (New  York,  1870)  devised  methods  of  duplex  signalling. 
Stark  (Vienna)  and  Bosscha  (Leyden,  1855)  invented  dipkx 
signalling,  and  Edison  (Newark,  N.  J.,  1874)  invented  quad- 
ruplex  telegraphy.  For  fast-speed  work  \Vheatstone  devised' his 
automatic  transmitter,  in  which  the  signs  which  represent  the 
letters  are  first  punched  by  machinery  on  strips  of  paper ;  these 
are  then  run  at  a  great  speed  through  the  transmitting  instru- 
ment, which  telegraphs  them  off  at  a  much  greater  rate  than  if 
the  separate  signals  were  telegraphed  by  hand.  Hughes  devised 
a  type-printing  telegraph.  Wheatstone  invented  an  ABC  tele- 
graph in  which  signals  are  spelled  by  a  hand  which  moves  over 
a  dial.  For  cable- working  Sir  W.  Thomson  invented  his  mirror 
galvanometer  and  his  delicate  siphon-recorder.  It  is  impossible 
in  these  Lessons  to  describe  more  than  one  or  two  of  the 
simpler  and  more  frequent  forms  of  telegraphic'  instruments. 
Students  desiring  further  information  should  consult  the  excel- 
lent manuals  on  Telegraphy  by  Messrs.  Preece  and  Sivewright, 
and  by  Mr.  Culley. 

424.  Single -Needle    Instrument. — The    single- 
needle  instrument  (Fig.   160)  consists  essentially  of  a 

vertical  galvan- 
ometer, in  which 
a  lightly  hung 
magnetic  needle 
is  deflected  to 
right  or  left 
when  a  current 
is  sent,  in  one 
direction  or  the 
other,  around  a 
coil  surrounding 
the  needle ;  the 
needle  visible  in 
front  of  the  dial 
is  but  an  index, 
A  code  of 


Fig.  160. 

the   real   magnetic   needle   being   behind. 


movements  agreed  upon  comprises  the  whole  alphabet 
in  combinations  of  motions  to  right  or  left.     In  order 


CHAP,  xri.]    ELECTRICITY  AND  MAGNETISM.          403 

to  send  currents  in  either  direction  through  the  circuit, 
a  "signalling-key"  or  "tapper"  is  usually  employed. 
The  tapper  at  one  end  of  the  line  works  the  instru- 
ment at  the  other ;  but  for  the  sake  of  convenience  it 
is  fixed  to  the  receiving  instrument.  In  Fig.  160  the 
two  protruding  levers  at  the  base  form  the  tapper,  and 
by  depressing  the  right  hand  one  or  the  left  hand  one, 
currents  are  sent  in  either  direction  at  will. 

The  principle  of  action  will  be  made  more  clear  by 
reference  to  Fig.  161,  which  shows  a  separate  signalling 
key.  The  two 
horizontal  levers 
are  respectively 
in  communica- 
tion with  the 
"line,"  and  with 
the  return  -  line 
through  "earth." 
When  not  in  use 

they  both  spring  Fig.  x6x. 

up  against  a  cross 
strip  of  metal  joined  to  the  zinc  pole  of  the  battery. 
Below  them  is  another  cross  strip,  which  communicates 
with  the  copper  (or  + )  pole  of  the  battery.  On 
depressing  the  "  line  "  key  the  current  runs  through  the 
line  and  back  by  earth,  or  in  the  positive  direction. 
On  depressing  the  "  earth  "  key  (the  line  key  remaining 
in  contact  with  the  zinc-connected  strip),  the  current 
runs  through  the  earth  and  back  by  the  line,  or  in  the 
negative  direction.  Telegraphists  ordinarily  speak  of 
these  as  positive  and  negative  currents  respectively. 

As  it  is  necessary  that  a  line  should  be  capable  of 
being  worked  from  either  end,  a  battery  is  used  at  each, 
and  the  wires  so  connected  that  when  at  either  end  a 
message  is  being  received,  the  battery  circuit  at  that  end 
shall  be  open.  Fig.  162  shows  the  simplest  possible 
case  of  such  an  arrangement.  At  one  end  is  a  battery 


404  ELEMENTARY  LESSONS  ON     [CHAP,  xn, 

zc,  one  pole  of  which  is  put  to  earth,  and  the  other  com- 
municates with  a  key  K.  This  key  is  arranged  (like  that 
in  Fig.  164),  so  that  when  it  is  depressed,  so  as  to  send 
a  signal  through  the  line,  it  quits  contact  with  the 
receiving  instrument  at  its  own  end.  The  current 
flowing  through  the  line  passes  through  K'  and  enters  a 


Fig.  162. 

receiving  instrument  G'  at  the  distant  end,  where  it  pro- 
duces  a  signal,  and  returns  by  the  earth  to  the  battery 
whence  it  started.  A  similar  battery  and  key  at  the 
distant  end  suffice  to  transmit  signals  in  the  opposite  - 
direction  to  G  when  K  is  not  depressed.  The  diagram 
is  drawn  as  if  G  were  a  simple  galvanometer  ;  but  the 
arrangement  would  perfectly  suit  the  Morse  instrument, 
in  which  it  is  only  required  at  either  end  to  send  long 
and  short  currents  without  reversing  the  direction. 

425.  The  Morse  Instrument. — The  most  widely 
used  instrument  at  the  present  day  is  the  Morse.  The 
Morse  instrument  consists  essentially  of  an  electro- 
magnet, which,  when  a  current  passes  through  its  coils, 
draws  down  an  armature  for  a  short  or  a  long  time. 


CHAP.  xii.J   ELECTRICITY  AND  MAGNETISM.          405 

It  may  either  be  arranged  as  a  "sounder"  in  which 
case  the  operator  who  is  receiving  the  message  listens 
to  the  clicks  and  notices  whether  the  intervals  between 
them  are  long  or  short;  or  it  may  be  arranged  as  an 
"  embosser"  to  print  dots  and  dashes  upon  a  strip  of  paper 
drawn  by  clockwork  through  the  instrument.  In  the 
most  modern  form,  however,  the  Morse  instrument  is 
arranged  as  an  "ink-writer"  in  which  the  attraction  of 
the  armature  downwards  lifts  a  little  inky  wheel  and 
pushes  it  against  a  ribbon  of  paper.  If  the  current  is 
momentary  it  prints  a  mere  dot.  If  the  current  con- 
tinues to  flow  for  a  longer  time  the  ribbon  of  paper  moves 
on.  and  the  ink-wheel  marks  a  dash.  The  Morse  code, 
or  alphabet  of  dots  and  dashes,  is  as  follows  : — 

A  .  —  K  —  .  —  U  .  .  — 

B— ...  L  .  —  .  .  v  .  .  .  — 

C  —  .  —  .  M W. 

D  — .  .  N  — .  X  —  .  .  — 

E  .  O Y  —  . 

F  .  .  —  .  P  . .  Z .  . 

G .  Q .  —  Full  stop 

H  .  .  .  .  R  .  —  .  Repetition  .  . 

I    .  .  S   .  .  .  Hyphen  —  ....— 

J   . T  —  Apostrophe  . . 

426.  Belay. — In  working  over  long  lines,  or  where 
there  are  a  number  of  instruments  on  one  circuit,  the 
currents  are  often  not  strong  enough  to  work  the 
recording  instrument  directly.  In.  such  a  case  there  is 
interposed  a  relay  or  repeater.  This  instrument  con- 
sists of  an  electromagnet  round  which  the  line  current 
flows,  and  whose  delicately  poised  armature,  when 
attracted,  makes  contact  for  a  local  circuit  in  which  a 
local  battery  and  the  receiving  Morse  instrument  are 
included.  The  principle  of  the  relay  is,  then,  that  a 
current  too  weak  to  do  the  work  itself  may  set  a  strong 
local  current  to  do  its  work  for  it. 


406 


ELEMENTARY  LESSONS  ON      [CHAP.  xil. 


In  Fig.  163  is  shown  a  Morse  instrument  (an  "em- 
bosser'^ M,  joined  in  circuit  with  a  local  battery  B,  and 


Earth 


•Line 


Line  Battery 


Fig.  163. 


a  relay.  Whenever  a  current  in  the  line  circuit  moves 
the  tongue  of  the  relay  it  closes  the  local  circuit,  and 
causes  the  Morse  to  record  either  a  dot  or  a  dash  upon 
the  strip  of  paper.  The  key  K  is  shown  in  an  enlarged 


Fig.  164. 

view  in  Fig.  164.  >  The  line  wire  is  connected  with  the 
central  pivot  A.  K  spring  f  keeps  the  front  .-end  of  the 
key  elevated  when  not  in  use,  sojthat  the  line  wire  is  in 


CHAP,  xii.]   ELECTRICITY  AND  MAGNETISM.  407 

communication  through  tl.e  rear  end  of  the  key  with  the 
relay  or  receiving  instrument.  Depressing  the  key  breaks 
this  communication,  and  by  putting  the  line  wire  in  com- 
munication with  the  main  battery  transmits  a  current 
through  the  line. 

427.  Faults   hi   Telegraph  Linea — Faults    may 
occur  in  telegraph  lines  fiom  several  causes  :  either  from 
the  breakage  of  the   wires  or  conductors,  or  from  the 
bieakage  of  the  insulators,   thereby  short-circuiting  the 
current  through  the  eaith  before  it  reaches  the  distant 
station,   or,   as   in  overhead    \\ires,  by    two  conducting 
wires  touching  one  another.      \rarious  modes  for  testing 
the  existence  and  position  of  faults  are  known  to  telegraph 
engineers ;  they  depend  upon  accurate  measurements  of 
resistance  or  of  capacity.    Thus,  if  a  telegraph  cable  part 
in  mid-ocean  it  is  possible  to  calculate  the  distance  from 
the  shore  end  to  the  broken  end  by  comparing  the  resist- 
ance that  the  cable  is  known  to  offer  per  mile  with  the 
resistance  offered  by  the  length  up  to  the  fault,  and  divid- 
ing the  latter  by  the  former. 

428.  Duplex  Telegraphy. — There'  are  two  distinct 
methods   of  arranging  telegraphic    apparatus    so  as  to 
transmit  two  messages  through  one  wire,  one  from  each 
end,  at  the  same  time.     The  first  of  these,  known  as 
the  differential  method,  involves  the  use  of  instruments 
wound  with  differential  coils,  and  is  applicable  to  special 
cases.     The  second  method  of  duplex  working,  known 
as  the  WheatstonJs  Bridge  Method,  is  capable  of  much 
more  general  application.      The  diagram  of  Fig.    165 
will    explain    the  general  principle.     The   first  require- 
ment in  duplex  working  is  that  the  instrument  at  each 
end   shall  only   move   in   response  to  signals  from  the 
other  end,   so   that   an   operator  at  R  may  be  able  to 
signal  to  the  distant   instrument    M'    without  his   own 
instrument  M  being  affected,   M  being  all  the  while  in 
circuit  and   able    to    receive    signals    from    the    distant 
operator    at    R'.      To    accomplish    this   the    circuit    is 


408 


ELEMEHTAI1Y  LESSONS  ON      [CHAP.  xn. 


divided  at  R  into  two  branches,  which  go,  by  A  and 
B  respectively,  the  one  to  the  line,  the  other  througi 
a  certain  resistance  P  to  the  earth.  If  the  ratio 
between  the  resistances  in  the  arms  RA  and  RB  is 
equal  to  the  ratio  of  the  resistances  of  the  line  and  of 
P,  then,  by  the  principle  of  Wheatstone's  Bridge,  no 
'current  will  pass  through  M.  So  M  does  not  show  any 
currents  sent  from  R ;  but  M'  will  show  them,  for  the 
current  on  arriving  at  C  will  divide  into  two  parts,  part 
flowing  round  to  the  earth  by  R',  the  other  part  flowing 


A 


Fig.  165. 


through  M'  and  producing  a  signal.  If,  while  this  is 
going  on,  the  operator  at  the  distant  R'  'depresses  his 
key  and  sends  an  equal  current  in  the  opposite  direction, 
the  flow  through  the  line  will  cease ;  but  M  will  now 
show  a  signal,  because,  although  no  current  flows 
through  the  line,  the  current  in  the  branch  RA  will 
now  flow  down  through  M,  as  if  it  had  come  from  the 
distant  R',  so,  whether  the  operator  at  R  be  signalling 
or  not,  M  will  respond  to  signals  sent  from  R'. 

The  Diplex  method  of  working  consists  in  sending 
two  messages  at  once  through  a  wire  in  the  same  direc- 
tion. To  do  this  it  is  needful  to  employ  instruments 
\\hich  work  only  with  currents  in  one  given  direction. 
The  method  involves  the  use  of  "  relays  "  in  which  the 
armatures  are  themselves  permanently  magnetised,  (or 
"  polarised "),  and  w*hich  therefore  respond  only  to 
currents  in  one  direction. 

The  Quadruples  method  of  working  combines  the 


CHAP.  XII.]    ELECTRICITY  AND  MAGNETISM.          409 


duplex  and  the  diplex  methods.  On  one  and  the  same 
line  are  used  two  sets  of  instruments,  one  of  which 
(worked  by  a  "polarised"  relay)  woiks  only  when  the 
direction  of  the  current  is  changed,  the  other  of  which 
(worked  by  a  non-polarised  relay  adjusted  with  springs 
to  move  only  with  a  certain  minimum  force)  work:;  only 
when  the  slretiglh  of  the  current  is  changed  and  is  inde- 
pendent of  their  direction. 

420.  Submarine  Telegraphy. — Telegraphic  com- 


Eig.  166. 

munication  between  two  countries  separated  by  a  Strait 
or  ocean  is  carried  on  through  cables,   sunk  to  the 

3  E 


410  ELEMENTARY  LESSONS  ON      [CHAP.  XH. 

bottom  of  the  sea,  which  carry  conducting  wires  care- 
fully protected  by  an  outer  sheath  of  insulating  and 
protecting  materials.  The  conductor  is  usually  of  purest 
copper  wire,  weighing ,  from  70  to  400  Ibs.  per  nauti- 
cal mile,  made  in  a  sevenfold  strand  to  lessen  risk 
of  breaking.  Fig.  166  shows,  in  their  natural  size, 
portions  of  the  Atlantic  cables  laid  in  1857  and  1866 
respectively.  In  the  latter  cable,  which  is  of  the  usual 
type  of  cable  for  long  lines,  the  core  is  protected  first  by 
a  stout  layer  of  guttapercha,  then  by  a  woven  coating  of 
jute,  and  outside  all  an  external  sheath  made  of  ten  iron 
wires,  each  covered  with  hemp.  The  shore  ends  are  even 
more  strongly  protected  by  external  wires. 

43O.  Speed  of  Signalling "  through  Cables. — 
Signals  transmitted  through  long  cables  are  retarded,  the 
retardation  being  due  to  two  causes. 

Firstly,  The  self-induction  of  the  circuit  may  prevent 
the  current  from  rising  at  once  to  its  height,  the  retarda- 
tion being  expressed  by  Helmh clt^s  equations,  given  in 
Art.  405. 

Secondly^  The  cable  in  its  insulating  sheath,  when 
immersed  in  water,  acts  like  a  Leyden  jar  of  enormous 
capacity  (as  explained  in  Art.  274),  and  the  first  portions 
of  the  current,  instead  of  flowing  through,  remain  in  the 
cable  as  an  electrostatic  charge.  For  every  separate 
signal  the  cable  must  be  at  least  partially  charged  and 
then  discharged.  Culley  states  that  vhen  a  current  is 
sent  through  an  Atlantic  cable  from  Ireland  to  New- 
foundland  rto  effect  is  produced  on  the  most  delicate 
instrument  at  the  receiving  end  for  two-tenths  of  a 
second,  and  that  it  requires  three  seconds  for  the  current 
to  gain  its  full  strength,  rising  in  an  electric  wave  which 
travels  forward  through  the  cable.  The  strength  of  the 
current  falls  gradually  also  when  the  circuit  is  broken. 
The  greater  part  of  this  retardation  is  due  to  electrostatic 
charge,  not  to  electromagnetic  self-induction ;  the  re- 
tardation  being  proportional  to  the  square  of  the  length 


CHAP,  xii.]    ELECTRICITY  AND  MAGNETISM.         411 

of  the  cable.     The  various  means  adopted  to  get  rid  of 
this  retardation  are  explained  in  Art.  275. 

431.  Receiving  Instruments  for  Cables. — The 
mirror-galvanometer  of  Sir  W.  Thomson  (Art.  202)  was 
devised  for  cable  signalling,  the  movements  of  the  spot 
of  light  sweeping  over  the  scale  to  a  short  or  a  long 
distance  sufficing  to  signal  the  dots  and  dashes  of  the 
Morse  code.     The  Siphon  Recorder  of  Sir  W.  Thomson 
is  an  instrument  which  writes  the  signals  upon  a  strip  of 
paper  by  the  following  ingenious  means : — The  needle 
part  of  a  powerful  and  sensitive  galvanometer  is  replaced 
by  a  fine  siphon  of  glass  suspended  by  a  silk  fibre,  one 
end  of  which  dips  into  an  ink  vessel     The  ink  is  spurted 
without  friction  upon  a  strip  of  paper  (moved  by  clock- 
work  vertically   past  the  siphon),   the   spurting  being 
accomplished  electrically  by  charging  the  ink  vessel  by 
a  continuous  electrophorus,  which  is  itself  worked  by  a 
small  electromagnetic  engine. 

LESSON  XL. — Electric  Bells,  Clocks^  and  Telephones. 

432.  Electric  Bells. — The  common  form  of  Electric 
Bell  or  Trembler  consists  of  an  electromagnet,  which 
moves  a  hammer  backward  and  forward  by  alternately 
attracting  and  releasing  it,  so  that  it  beats  against  a  bell. 
The  arrangements  of  the  instrument  are  shown  in  Fig. 
1 67,  in  which  E  is  the  electromagnet  and  H  the  hammer. 
A  battery,  consisting  of  one  or  two  Ledanchd  cells  placed 
at  some  convenient  point  of  the  circuit,  provides  a  current 
when  required.     By  touching  the  "  push  "  P,  the  circuit 
is  completed,  and  a  current  flows  along  the  line  and 
round  the  coils  of  the  electromagnet,  which  forthwith 
attracts  a  small  piece  of  soft  iron  attached  to  the  lever, 
which  terminates  in  the  hammer  H.     The  lever  is  itself 
included  in. the  circuit,  the  <*irrent  entering  it  above  and 
quitting  it  at  C  by  a  contact-breaker,  consisting  of  a 
spring  tipped  with  platinum  resting  against  the  platinum 


412 


ELEMENTARY  LESSONS  ON      [CHAP.  xn. 


tip  cf  a  screw,  from  which  a  return  wire  passes  back  to 
the  zinc  pole  of  the  battery. .  As  soon  as  the  lever  is 
attracted  forward  the  circuit  is  broken  at  C  by  the  spring 
moving  away  from  contact  with  the  screw;  hence  the 
current  stops,  and  the  electromagnet  ceases  to  attract  the 
armature.  The  lever  and  hammer  therefore  fall  back, 


Fig.  167, 

again  establishing  contact  at  C,  whereupon  the  hammer 
is  once  more  attracted  forward,  and  so  on.  The  push 
P  is  shown  in  section  on  the  right  of  Fig.  167.  It 
usually  consists  of  a  cylindrical  knob  of  ivory  or  porcelain 
capable  of  moving  loosely  through  a  hole  in  a  circular 
support  of  porcelain  or  wood,  and  which,  when  pressed, 
forces  a  platinum -tipped  spring  against  a  metal  pin,  and 
£O  makes  electrical  contact  between  the  two  parts- of  the 
interraptecl  circuit 

433,  Electric  Clocks. — Clocks  may  be  either  driven 
or  controlled  by  electric  currents.  Bain,  Hipp,  and 
others,  have  devised  electric  clocks  of.  the  first  kind,  in 
.which  the  ordinary  motive  power  of  a  weight  or  spring  is- 


CHAP.  XII.]    ELECTRICITY  AND  MAGNETISM.         41 3 

~~~"~~~  • 

abandoned,  the  clock  being  driven  by  its  pendulum,  the 
"  bob  "  of  which  is  an  electromagnet  alternately  attracted 
from  side  to  side.  The  difficulty  of  maintaining  a  perfectly 
constant  battery  current  has  prevented  such  clocks  from 
coming  into  use. 

Electrically  controlled  clocks,  governed  by  a  standard 
central  clock,  have  proved  a  more  fruitful  invention.  In 
these  the  standard  timekeeper  is  constructed  so  as  to 
complete  a  circuit  periodically,  once  every  minute  or  hall 
minute.  The  transmitted  currents  set  in  movement  the 
hands  of  a  system  of  dials  placed  at  distant  points,  by 
causing  an  electromagnet  placed  behind  each  dial  to 
attract  an  armature,  which,  acting  upon  a  ratchet  wheel 
by  a  pawl,  causes  it  to  move  forward  through  one  tocth 
at  each  specified  interval,  and  so  carries  the  hands  round 
at  the  same  rate  as  those  of  the  standard  clock. 

Electric  chronographs  are  used  for  measuring  very  small  in- 
tervals of  time.  A  style  fixed  to  the  armature  of  an  electro- 
magnet traces  a  line  upon  a  piece  of  paper  fixed  to  a  cylindei 
revolving  by  clockwork.  A  current  sent  through  the  coils  of 
the  electromagnet  moves  the  ar.nature  and  causes  a  lateral  notch 
in  the  line  so  traced.  Two  currents  are  marked  by  two  notches  ; 
and  from  th«  interval  of  space  between  the  two  notches  the  in- 
terval of  time  which  elapsed  between  the  two  currents  may  be 
calculated  to  the  ten-thousandth  par.  of  a  second  if  the  speed 
of  rotation  is  accurately  known.  The  velocity  with  which  a 
cannon  ball  movej  along  the  bore  of  the  cannon  can  be  measured 
thus. 

434.  Electric  Telephones — The  first  successful 
attehiot  to  transmit  sounds  electrically  was  made  in 
1 86 1  by  Reis,  who  succeeded  in  conveying  musical  and 
other  tones  by  an  iniperfeci  telephone.  In  this  instru- 
ment the  voice  was  cau^et.!  to  act  upon  a  point  of  loose 
contact  in  an  electric  circuit,  and  by  bringing  those  parts 
into  greater  or  less  intimacy  of  contact  (Art.  346),  thereby 
varied  the  resistance  offered'  to  the  circuit.  The  trans- 
mitting part  of  Reis's  telephone  consisted  of  a  battery 
and  a  contact-breaker,  the  latter  being  formed  of  a  tym- 


4H  ELEMENTARY  LESSONS  ON         [CHAP,  xn 

panum  or  diaphragm  of  stretched  membrane,  capable  of 
taking  up  sonorous  vibrations,  and  having  attached  to 
it  a  thin  elastic  strip  of  platinum,  which,  as  it  vibrated, 
beat  to  and  fro  against  the  tip  of  a  platinum  wire,  so 
making  and  breaking  contact  wholly  or  partially  at  each 
vibration  in  exactly  the  same  manner  as  is  done  with  the 
carbon  contacts  in  the  modern  transmitters  of  Blake, 
Berliner,  etc.  The  receiving  part  of  the  instrument 
consisted  of  an  iron  wire  fixed  upon  a  sounding-board 
and  surrounded  by  a  coil  of  insulated  wire  forming  part 
of  the  circuit.  The  rapid  magnetisation  and  demag- 
netisation of  such  an  iron  core  will  produce  audible 
sounds  (Art.  113),  which,  since  the  pitch  of  a  note 
depends  only  on  the  frequency  and  not  on  the  form  or 
amplitude  of  the  vibrations,  will  reproduce  the  pitch  of  a 
note  sung  into  the  transmitting  part.  If  the  current  vary 
less  abruptly,  the  iron  wire  is  partially  magnetised  and 
demagnetised,  giving  rise  in  turn  to  vibrations  of  varying 
amplitudes  and  forms ;  hence  such  a  wire  will  serve 
perfectly  as  a  receiver  to  reproduce  speech  if  a  good 
transmitter  is  used.  Reis  himself  transmitted  speech 
with  his  instrument,  but  only  imperfectly,  for  all  tones 
of  speech  cannot  be  transmitted  by  abrupt  interruptions 
of  the  current,  to  which  Reis's  transmitter  is  prone  when 
spoken  into,  owing  to  the  extreme  lightness  of  the  con- 
tact :  they  require  gentle  undulations,  sometimes  simple, 
sometimes  complex,  according  to  the  nature  of  the  sound. 
The  vowel  sounds  are  produced  by  periodic  and  complex 
movements  in  the  air  ;  the  consonants  being  for  the  most 
part  non-periodic.  If  the  parts  in  contact  be  not  loo 
light,  and  speech  be  not  too  loud,  Reis's  transmitter 
works  fairly  as  a  transmitter,  the  platinum  contacts  when 
clean  serving  as  a  satisfactory  current-regulator  to  vary 
the  current  in  proportion  to  the  vibrations  of  the  voice. 

Reis  also  devised  a  second  receiver,  in  v/hich  an  clcctro-magncl 
attracted  an  elastically-supported  armature  of  iron,  which  vibrated 
under  the  attraction  of  the  more  or  less  interrupted  current. 


CHAP,  xii.]   ELECTRICITY  AND  MAGNETISM.         415 


435.  Graham  Bell's  Telephone. — In  1876  Graham 
Beil  invented  the  magneto-telephone.  In  this  instrument 
the  speaker  talks  to  an  elastic  plate  of  thin  sheet  iron, 
which  vibrates  and  transmits  its  every  movement  electric- 
ally to  a  similar  platejrt  a  similar  telephone  at  a  distant 
station,  causing  it  to  vibrate  in  an  identical  manner,  and 
therefore  to  emit  identical  sounds.  The  transmission  of 
the  vibrations  depends  upon  the  principles  of  magneto- 
electric  induction  explained  in  Lesson  XXXVI.  Fig. 
1 68  shows  Bell's  Tele- 
phone in  it£  latest  form, 
and  its  internal  parts  in 
section.  The  disc  D  is 
placed  behind  a  conical 
mouthpiece,  to  which  the 
speaker  places  his  mou^th 
or  the  hearer  his  ear. 
Behind  the  disc  is  a  mag- 
net AA  running  the  length 
of  the  instrument";  and 
upon  its  front  pole,  w£ich 
nearly  touches  the  disc, 
is  fixed  a  small  bobbin, 
on  which  is  wound  a  coil  C  of  fine  insulated  wire,  the 
ends  of  the  coil  being  connected  with  the  terminal  screws 
F  F.  One  such  inslrurr\ent  is  used  to  transmit,  and  one 
to  receive,  the  sounds,  the  two  telephones  being  con- 
nected in  simple  circuit.  No  battery  is  needed,  for  the 
transmitting  instrument  itself  generates  the  induced 
currents  as  follows  :  The  magnet  AA  induces  a  certain 
number  of  lines-of-force'  through  the  coil  C.  Many  of 
these  pass  into  the  iron  disc.  When  the  iron  disc  in 
vibrating  moves  towards  the  magnet-pole,  more  lines-of 
force  meet  it ;  when  it  recedes,  fewer  lines-of-force  meet 
it  Its  motion  to  and  fro  will  therefore  alter  the  number 
of  1  hi  es-of -force  which  pass  through  the  hollow  of  the  coil 
C,  and  will  therefore*  (Art.  394)  generate  in  the  wire  of 


Fig.  168. 


4i6  ELEMENTARY  LESSONS  ON        [CHAP.  xii. 

the  coils  currents  whose  strength  is  proportional  to  the 
rate  of  change  in  the  number  of  the  lines-of-force  which 
pass  through  the  coil  Bell's  telephone,  when  used  as 
a  transmitter,  may  therefore  be  regarded  as  a  sort  of 
magneto-electric  generator,  which,  by  vibrating  to  and 
fro,  pumps  currents  in  alternate  directions  into  the  wire. 
At  the  distant  end  the  currents  as  they  arrive  flow  round 
the  coils  either  in  one  direction  or  the  other,  and  there- 
fore either  add  momentarily  to  or  take  from  the  strength 
of  the  magnet.  When  the  current  in  the  coils  is  in  such 
a  direction  as  to  reinforce  the  magnet,  the  magnet  attracts 
the  iron  disc  in  front  of  it  more  strongly  than  before.  If 
the  current  is  in  the  opposite  direction  the  disc  is  less 
attracted  and  flies  back.  Hence,  whatever  movement  is 
imparted  to  the  disc  of  the  transmitting  telephone,  the 
disc  of  the  distant  receiving  telephone  is  forced  to  repeat, 
and  it  therefore  throws  the  air  into  similar  vibrations, 
and  so  reproduces  the  sound.  Bell's  Telephone,  used 
as  a  receiver,  differs  only  from  the  second  receiver  of 
Rcis  in  having  as  its  armature  a  thin  elastic  iron  plate 
instead  of  an  iron  bar  oscillating  on  an  elastic  support, 
and  in  having  its  central  magnet  of  steel  instead  of 
iron. 

436.  Edison's  Telephone. — Edison  constructed  a 
telephone  for  transmitting  speech,  in  which  the  vibrations 
of  the  voice,  actuating  a  diaphragm  of  mica,  made  it 
exert  more  or  less  compression  on  a  button  of  prepared 
lamp-black  placed  in  the  circuit.  The  resistance  of  this 
is  affected  by  pressure  of  contacts ;  hence  the  varying 
pressures  due  to  the  vibrations  cause  the  button  to  offer 
a  varying  resistance  to  any  current  flowing  (from  a  battery) 
in  the  circuit,  and  vary  its  strength  accordingly.  This 
varying  current  may  be  received  as  before  in  an  electro- 
magnetic receiver  of  the  type  described  above,  and  there 
set  up  corresponding  vibrations.  Edison  has  also  in- 
vented a  Telephone  Receiver  of  singular  power,  which 
depends  upon  a  curious  fact  discovered  by  himself,  namely, 


CHAP,  xii.]    ELECTRICITY  AND  MAGNETISM.         417 


that  if  a  platinum  point  presses  against  a  rotating  cylinder 
of  moist  chalk,  the  friction  is  reduced  when  a  current 
passes  between  the  two.  And  if  the  point  be  attached 
to  an  elastic  disc,  the  latter  is  thrown  into  vibrations 
corresponding  to  the  fluctuating  currents  coming  from 
the  speaker's  transmitting  instrument. 


Fig.  169. 

438  (bis).  Dolbear's  Telephone. — Telephone  Re- 
ceivers have  also  been  invented  by  Varley  and  Dolbear, 
in  which  the  attraction  between  the  oppositely-electrified 
armatures  of  a  condenser  is  utilised  in  the  production  of 
sounds.  The  transmitter  is  .placed  in  circuit  with  the 
primary  wire  of  a  small  induction-coil ;  the  secondary 
wire  of  this  coil  is  united  through  the  line  to  the  receiving 
condenser.  In  Dolbear's  telephone  the  receiver  consists 
merely  of  two  thin  metal  discs,  separated  by  a  very  thin 
air-space,  and  respectively  united  to  the  two  ends  of  the 
secondary  coil:  As  the  varying  currents  flow  into  and 
out  of  this  condenser  the  two  discs  attract  one  another 
more  or  less  strongly,  and  thereby  vibrations  are  set 


4i8  ELEMENTARY  LESSONS  ON         [CHAP,  X!i, 

up  which  correspond  to  the  vibrations  of  the  original 
sound. 

437.    Hughes'   Microphone. — Hughes,    in    1878, 
discovered  that  a  loose  contact  between  two  conductors, 
forming  part  of  a  circuit  in  which  a  small  battery  and  a 
receiving  telephone  are  included,  may  serve  to  transmit 
sounds  without  the  intervention  of  any  specific  tympanum 
or  diaphragm  like  those  of  Reis  and  Edison,  because  the 
smallest  vibrations  will  effect  the  amount  of  the  resistance 
at  the  point  of  loose-contact,  if  the  latter  be  delicately 
set.     The  Microphone  (Fig.  169)  embodies  this  prin- 
ciple.     In  the  form  shown  in  the  figure,  a  small  thin 
pencil  of  carbon  is  supported  loosely  between  two  little 
blocks  of  the  same  substance-  fixed  to  a  sounding-board 
of  thin  pine-wood,  the  blocks  being  connected  with  one 
or  two  small  cells  and  a  Bell  telephone  as  a  receiver. 
The  amplitude  of  the  vibrations  emitted  by  this  telephone 
may  be  much  greater  than  those  of  the  original  sounds, 
and  therefore  the  microphone  may  serve,  as  its  name 
indicates,  to  magnify  minute  sounds,  such  as  the  ticking 
of  a  watch  or  the  footfalls  of  an  insect,  and  render  them 
audible.      The  less  sensitive  carbon- transmitters^  used 
frequently  in  conjunction  with  the  telephone,  are  some- 
times regarded  as  varieties  of  the  microphone.     In  some 
of  these  instruments — Blake's,  for  instance— there  is  a 
tympanum    like   that    of  Edison's    and  of  Reis's  tele- 
phone. 

438.  Hughes'  Induction  Balance. — The  extreme 
sensitiveness  of  Bell's  telephone  (Art.  435)  to  the  feeblest 
currents  has  suggested  its  employment  to  detect  currents 
too  weak  to  affect  the  most  delicate  galvanometer.  The 
currents  must,  however,  be  intermittent,  or  they  will  not 
keep  the  disc  of  the  telephone  in  vibration.  Hughes 
applied  this  property  of  the  telephone  to  an  instrument 
named  the  Induction  Balance  (Fig.  170)-  A  small 
battery  B,  connected  with  a  microphone  M,  passes 
through  two  coils  of  wire  PI,  P,,  wound  on.  bobbins  fixed 


CHAP,  xii.]  ELECTRICITV  AND  MAGNETISM.         419 

on  a  suitable  stand.  Above  each  of  these  primary  coils 
are  placed  two  secondary  coils,  Si,  S2,  of  wire,  of  the 
same  size,  and  of  exactly  equal  numbers  of  turns  of  wire. 
The,  secondary  coils  are  joined  to  a  telephone  T,  and 
are  Wound  in  opposite  directions.  The  result  of  this 
arrangement  is  that  whenever  a  current  either  begins  or 
stops  flowing  in  the  primary  coils,  PI  induces  a  current 
in  Sj,  and  Ps  in  S^.  As  Sj  and  S2  are  wound  in  opposite 
ways,  the  two  currents  thus  induced  in  the  secondary 
wire  neutralise  one  another,  and,  if  they  are  of  equal 
strength,  balance  one  another  so  exactly  that  no  sound 


Pig.  170. 

is  heard  in  the  telephone.  But  a  perfect  balance  cannot 
T>e  obtained  unless  the  resistances  and  the  co-efficients  of 
mutual  induction  and  of  self-induction  are  alike.  If  a  flat 
piece  of  silver  or  copper  (such  as  a  coin)  be  introduced 
between  Sj  and  Px,  there  will  be  less  induction  in  Si  than 
in  S2,  for  part  of  the  inductive  action  in  Pl  is  now  spent 
on  setting  up  currents  in  the  mass  of  the  metal  (Art.  401), 
and  a  sound  will  again  be  heard  in  the  telephone.  But 
balance  can  be  restored  by  moving  S8  farther  away  from 
PS,  until  the  induction  in  S2  is  reduced  to  equality  with 
Si,  when  the  sounds  in  the  telephone  again  cease.  It  is 
possible  by  this  means  to  test  the  relative  conductivity  of 
different  metals  which  are  introduced  into  the  coils.  It 
is  even  possible  to  detect  a  counterfeit  coin  by  the  indi- 


420 


ELEMENTARY  LESSONS.         [CHAP.  xn. 


cation  thus  afforded  of  its  conductivity.  The  induction 
balance  has  also  been  applied  in  surgery  by  Graham 
Bell  to  detect  the  presence  of  a  bullet  in  a  wound,  for  a 
lump  of  metal  may  disturb  the  induction  when  some 
inches  distant  from  the  coils. 


Fig.  171. 


439.  Hughes'  Magnetic  Balance. — A  very  con- 
venient instrument  for  testing  the  magnetic  properties 
of  different  specimens  of  iron  and  steel  was  devised  by 
Hughes  in  1884.  The  sample  to  be  tested  is  placed  in 
a  magnetising  coil  A  (Fig.  171),  and  a  current  is  sent 
round  it  It  deflects  a  lightly-suspended  indicating 
needle  B,  which  is  then  brought  to  zero  by  turning  a 
large  compensating  magnet  M  upon  its  centre.  A  small 
coil  C  is  added  to  balance  the  direct  deflecting  effect 
due  to  coil  A.  The  author  of  this  book  has  shown  that 
if  the  distance  from  M  to  B  is  2-3  times  the  length  of 
M,  the  angle  through  which  M  is  turned  is  proportional 
to  the  magnetic  force  due  to  the  iron  core  at  A,  provided 
the  angle  is  less  than  60°. 


PROBLEMS  AND  EXERCISES.  421 


PROBLEMS  AND  EXERCISES. 

QUESTIONS  ON  CHAPTER  I. 

1.  From  what  is  the  word  "  electricity"  derived? 

2.  Name  some  of  the  different  methods  of  producing  electri- 
fication. 

3.  A-body  is  charged  so  feebly  that  its  electrification  will  not 
perceptibly  move  the  leaves  of  a  gold-leaf  elect loscope.     Can 
you  suggest  any  means  of  ascertaining  whether  the  charge  of  the 
body  is  positive  or  negative  ? 

4.  Describe  an  experiment  to  prove  that  moistened  thread 
conducts  electricity  better  than  dry -thread. 

5.  Why  do  we  regard   the  two  electric  charges  produced 
simultaneously  by   rubbing   two  bodies  together  as  being   ot 
opposite  kinds  ? 

6.  Explain  the  action  of  the  elcctrophorus.     Can  you  suggest 
any  means  for  accomplishing  by  a  rotatory  motion  the  operations 
of  lifting  up  and  down  the  co?er  of  the  instrument  so  as  to  obtain 
a  continuous  supply  instead  of  an  intermittent  one. 

7.  Explain  the  Torsion  Balance,  and  how  it  can  be  used  to 
investigate  the  laws  of  the  distribution  of  electricity. 

8.  Two  small  balls  are  charged   respectively  with  +  24  and 
—  8  units  of  electricity.     V/ith  what  foice  will  they  attract  one 
another  when  placed  at  a  distance  of  4  centimetres  from  one 
another?  Atu.    12  dynes. 

9.  If  these  two  balls  are  then  made  to  touch  for  an  instant 


422  PROBLEMS  AND  EXERCISES. 

and  then  put  biack  in  their  former  positions,  with  what  force 
will  they  act  on  each  other  ? 

Ans.  They  repel  one  another  with  a  force  of  4  dynes. 

10.  Zinc  filings  are  sifted  through  a  sieve  made  of  copper  wire 
upon  an  insulated  zinc  plate  joined  by  a  wire  to  an  electroscope. 
What  will  be  observed  ? 

1 1.  Explain  the  principle  of  an  air-condenser  ;  and  state  why 
it  is  that  the  two  oppositely  charged  plates  show  less  signs  of 
electrification  when  placed  near  together  than  when  drawn  apart 
from  one  another. 

12.  There  are  four  Leyden  jars  A,  B,  C*  and  D,  of  which  A, 
B,  and  D,  are  of  glass,  C  of  guttapereha.     A,  B,  and  C,  are  of 
the  same  size,  D  being  just  twice  as  tall  and  twice  as  wide 
as  the  others.     A,  C,  ~and  D,  are  of  the   same  thickness  of 
material,  but  B  is  made  of  glass  only  half  as  thick  as  A  or  D 
Compare  their  capacities.  Ans.  Take  capacity  of  A  as  I 

that  of  B  will  be  2 
that  of  C  will  be  \ 
and  that  of  D  will  be  4. 

13.  How  would  you  prove  that  there  is  no  electrification 
within  a  closed  conductor  ? 

14.  What  prevents  the  charge  of  a  body  from  escaping  away 
at  its  surface  ? 

1 5.  Explain  the  action  of  Hamilton's  mill. 

1 6.  Two  brass  balls  mounted  on  glass  stems  are  placed  half 
an  inch  apart..     One  of  them  is  gradually  charged  by  a  machine 
until  a  spark  passes  between  the  two  balls.     State  exactly  what 
happened  in  the  other  brass  ball  and  in  the  intervening  air  up 
to  the  moment  of  the  appearance  of  the  spark. 

17.  Define  electric  density.     A  charge  of  248  units  of  elec- 
tricity was  imparted  .to  a  sphere  of  4  centims.  radius.     What  is 
the  density  of  the  charge  ?  Ans.    1*23  nearly. 

QUESTIONS  ON  CHAPTER  II. 

I.  A  dozen  steel  sewing-needles  are  hung  in  a  bunch  by 
threads  through  their  eyes.  How  will  they  behave  when  hung 
over  the  pole  of  a  strong  magnet  ? 


PROBLEMS  AND  EXERCISES.  423 

^  2.  Six  magnetised  sewing-needles  are  thrust  vertically  through 
six  little  floats  of  cork,  and  are  placed  in  a  basin  of  water  with 
their  N. -pointing  poles  upwards.  How  will  they  affect  one 
another,  and  what  will  be  the  effect  of  holding  over  them  the 
S.  -pointing  pole  of  a  magnet  ? 

3.  What   distinction   do   you    draw   between   magnets  an^. 
magnetic  matter  ? 

4.  On  board  an  iron  ship  which  is  laying  a  submarine  tele- 
graph cable  there  is  a  galvanometer  used  for  testing  the  continuity 
of  the  cable.      It  is  necessary 'to  screen  the  magnetised  needle  of 
the  galvanometer  from  being  affected  by  the  magnetism  of  the 
ship.     How  can  this  be  done  ? 

5.  How    would   you   prove   two   magnets   to   be   of  equal 
strength  ? 

6.  The   force   which   a   magnet-pole    exerts    upon   another 
magnet-pole   decreases   as  you   increase   the   distance    between 
them.     What  is  the  exact  law  of  the  magnetic  force,  and  how 
is  it  proved  experimentally  ? 

7.  What  force  does  a  magnet-pole,  the  strength  of  which  .is 
9  units,  exert  upon  a  pole  whose  strength  is  16  units  placed 
6  centimetres  away?  Ans.  4  dynes. 

8.  A  pole  of  strength  40  units  acts  with  a  force  of  32  dynes 
upon  another  pole  5  centimetres  awav.     What  is  the  strength 
of  that  pole  ?  Ans.   20  units. 

9.  It  is  desired  to  compare  the  magnetic  force  at  a  point  10 
centimetres  from  the  pole  of  a  magnet  with  the  magnetic  force 
at  5  centimetres'  distance.     Describe  four  ways  of  doing  this. 

I  o.   Explain  the  phenomenon  of  Consequent  Poles. 

n.  In  what 'direction  do  the  lines  of  magnetic  induction  (or 
"lines  of  force")  run  in  a  plane  in  which  there  is  a  single 
magnetic  pole  ?  How  would  you  arrange  an  experiment  by  which 
to  test  your  answer  ? 

12.  What  is  a  Magnetic  Shell  1     What  is  the  law  of  the 
potential  due  to  a  magnetic  shell  ? 

13.  A  steel  bar  magnet  suspended  horizontally,  and  set  to 
oscillate   at  Bristol,   made    iio   complete   oscillations   in   five 


424  PROBLEMS  AND  EXERCISES. 

minutes ;  the  same  needle  when  set  oscillating  horizontally  at 
St.  Helena  executed  112  complete  oscillations  in  four  minutes. 
Compare  the  horizontal  component  of  the  force  of  the  earth's 
magnetism  at  Bristol  with  that  at  St.  Helena. 

Ans.   H  at  Bristol :  H  at  St.  Helena  ::  484  :  784 

£4.   Supposing  the  dip  at  Bristol  to  be  70°  and  that  at  St. 

Helena  to  be   30°,  calculate  from  the  data  of  the  preceding 

question  the  total  force  of  the  earth's  magnetism  at  St  Helena, 

that  at  Bristol  being  taken  as  '48  unit.  Ans.   "307. 

[N.B. — The  student  should  see  Footnote  i,  on  p.  116.] 

15.  A  small  magnetic  needle  was  placed  magnetically  north 
of  the  middle  point  of  a  strong  bar-magnet  which  lay  (magneti- 
cally) cast  and  west.     When  the  magnet  was  3  feet  away  from 
the  needle  the  deflexion  of  the  latter  was  2° ;  when  moved  up 
to  a  distance  of  2  feet  the  deflexion  was  6°  30' ;  and  when  only 
I  foot  apart  the  deflexion  was  43°.     Deduce  the  law  of  the  told 
action  of  one  magnet  on  another. 

1 6.  Describe  how  the  daily  irregularities  of  the  earth's  mag- 
netism are  registered  at  different  static:- v.  for  comparison. 


QUESTIONS  ON  CHAPTER  III. 

1.  Show  that  the  total  of  the  differences  of  potential  by  con- 
tact  in  three  simple  voltaic  cells  joined  in  series  is  three  times  as 
great  as  the  difference  of  potential  in  one  cell,   the  materials 
being  the  same  in  each. 

2.  How  can  local  action  and  polarisation  be  prevented  in  a 
voltaic  cell  ? 

3.  Supposing  the  length  of  spark  to  be  proportional  to  the 
difference  of  potential,  calculate  from  the  data  of  Arts.  291  and 
178  how   many  Daniell's  cells  would  be  required  to  yield  a 
sufficient  difference  of  potential  to  produce  a  spark  one  mile  long 
through  air.  Ans.  1692  million  cells. 

4.  On  '.vhat  does  the  internal  resistance  of  a  battery  depend  ? 
Is  there  any  way  of  diminishing  it  ? 

5.  Twenty -four  similar  cells  are  grouped   together  in  four 
row*  of  six  ceils  each  ;  compare  the  electromotive-force  and  the 


PROBLEMS  AND  EXERCISES.  425 

resistance  of  the  battery  thus  grouped,  with  the  electromotive- 
force  and  the  resistance  of  a  single  cell. 

Ans.  The  E.M.F.  of  the  battery  is  six  times  that  of 

one  cell.     The  total  internal  resistance  is  one  and 

a  half  times  that  of  one  cell. 

6.  A  piece  of  silk-covered  copper   wire  is  coiled  round  the 
equator  of  a  model  terrestrial  globe.     Apply  Ampere's  rule  to 
determine  in  which  direction  a  current  must  be  sent  through  the 
coil  in  order  that  the  model  globe  may  represent  the  condition 
of  the  earth  magnetically. 

Ans.  The  current  must  flow  across  the  Atlantic  from 
Europe  to  America,  and  across  the  Pacific  from 
America  toward  India  ;  or,  in  other  words,  must 
flow  always  from  east  toward  west.- 

7.  A  current  of  '24  amperes  flows  through  a  circular  coil  of 
seventy-two  turns,  the  (average)  diameter  of  the  coils  being  20 
centimetres.        What  is  the  strength  of  the  magnetic  field  which 
the  current  produces  at  the  centre  of  the  coil  ? 

Ans.    i  -08. 

8.  Suppose  a  current  passing  through  the  above  coil  produced 
a  deflection  of  35°  upon  a  small  magnetic  needle  placed  at  its 
centre  (the  plane  of  the  coils  being  in  the  magnetic  meridian), 
at   a   place   where   the   horizontal   component   of  the   earth's 
magnetic    force    is    "23    units.     Calculate  the  strength  of  the 
current  in  amperes.      (Art.  200.)  Ans.  O'O35. 

9.  The  current  generated  by  a  dynamo-electric  machine  was 
passed  through  a  large  ring  of  stout  copper  wire,  at  the  centre 
of  which  hung  a  small  magnetic  needle  to  serve  as  a  tangent 
galvanometer.      When  the  steam  engine  drove  the  armature  of 
the  generator  at  450  revolutions  per  minute  the  deflection  of  the 
needle  was  60°.      When  the  speed  of  the  engine  was  increased 
so  as  to  produce  900  revolutions  per  minute  the  deflection  was 
74°.     Compare  the  strength  of  the  currents  in  the  two  cases. 

Ans.  The  current  was  twice  as  great  as  before,  for  tan 
74°  is  almost  exactly  double  of  tan  60°, 

10.  The  current  from  two  Grove's  cells  was  passed  through 
a  sine  -  galvanometer  to  measure  its  strength.     When  the  con- 
ducting wires  were  of  stout  copper  wire  the  coils  had  to  be 
turned  through  70°  before  they  stood  parallel  to  the  needle. 
But  when  long  thin  wires  were  used  as  conductors  the  coil$ 

.  2  F 


426  PROBLEMS  AND  EXERCISES. 

only  required  to  be  turned  through  9°.  Compare  the  strength 
of  the  current  in  the  first  case  with  that  in  the  second  case 
when  flowing  through  'the  thin  wires  which  offered  considerable 
resistance.  Ans.  Currents  are  as  I  to  |,  or  as  6  to  I. 

-if 

II.  A  plate  of  zinc  and  a  plate  of  copper  are  respectively 
united  by  copper  wires  to  the  two  screws  of  a  galvanometer. 
They  were  then  dipped  side  by  side  into  a  glass  containing 
dilute  sulphuric  acid.  The  galvanometer  needle  at  first  showed 
a  deflection  of  28°,  but  five  minutes  later  the  deflection  had 
fallen  to  11°.  How  do  you  account  for  this  failing  off? 

^12.  Classify  liquids  according  to  theh1  power  of  conducting 
electricity. 

13.  Name  the  substances  produced  at  the  anode  and  kathode 
respectively  during  the  electrolysis  of  the  following  substances  :  — 
Water,  dilute  sulphuric   acid,  sulphate  of  copper  (dissolved  in 
water),  hydrochloric  acid  (strong),  iodide  of  potassium  (dissolved 
in  water),  chloride  of  tin  (fused). 

14.  A  current  is  sent  through  three  electrolytic  cells,  the  first 
containing  acidulated  water,  the  second  sulphate  of  copper,  the 
third  contains  a  solution  of  silver  in  cyanide  of  potassium.    How 
much  copper  will  have  been  deposited  in  the  second  cell  while 
2  -268  grammes  of  silver  have  been  deposited  in  the  third  cell  ? 
And  what  volume  of  mixed  gases  will  have  been  given  off  at  the 
same  time  in  the  first  cell  ? 

Ans.   '6614  grammes  of  copper  and  3$2'S  cubic  centi- 
metres of  mixed  gases. 

15.  A  current  passes  by  platinum  electrodes  through  three 
cells,  the  first  containing   a   solution    of  blue   vitriol   (cupric 
sulphate),   the  second  containing  a   solution  of  green   vitriol 
(ferrous   sulphate),    the   third  containing   a  solution  of  ferric 
chloride.     State  the  amounts  of  the  different  substances  evolved 
at  each  electrode  by  the  passage  of  1000  coulombs  of  electricity 

KSrtt  r,!7      \  Anode  -0828  gramme  of  oxygen  gas.- 

*'y  I  Kathode  -3261  gramme  of  copper. 
c       J  r  11  \  Anode  '0828  gramme  of  oxygen. 
**•  \  Kathode  -2898  gramme  of  iron. 


r.ii    \  A110^  *3675  gramme  of  chlorine. 
'*"'   I  Kathode  -1449  gramme  of  iron. 

1  6.  A  tangent  galvanometer,  whose  '  '  constant  "  in  absolute 
units  was  0*080,  was  joined  in  circuit  with  a  battery  and  an 


PROBLEMS  AND  EXERCISES.  42? 

electrolytic  cell  containing  a  solution  of  silver.  The  current 
was  kept  on  for  one  hour  ;  the  deflection  observed  at  the  begin- 
ning was  36°,  but  it  fell  steadily  during  the  hour  to  34°.  Sup- 
posing the  horizontal  component  of  the  earth's  magnetic  force 
to  be  '23,  calculate  the  amount  of  silver  deposited  in  the  cell 
during  the  hour,  the  absolute  electro  -  chemical  "equivalent  of 
silver  being  jo 'Oil  34.  Ans.  '526  gramme. 

17.  A  piece  of  zinc,  at  the  lower  end  of  which  a  piece  of 
copper  wire  is  fixed,  is  suspended,  in  a  glass  jar  containing  a 
solution  of  acetate  of  lend.     After  a  few  hours  'a  deposit  of 
lead    in    a   curious    tree -like   form   ("Arbor  Saturni")  grows 
downwards  from  the  copper  wire.     Explain  this. 

1 8.  Explain  the  conditions  under   which   electricity  excites 
muscular  contraction.      How  can  the  converse  phenomenon  of 
currents  of  electricity  produced    by  muscular-  contraction   be 
shown  ? 


QUESTIONS  ON  CHAPTER  IV. 

1.  Define  the  untt  of  electricity  as  derived  in  absolute  terms 
from  the  fundamental  units  of  length,  MOSS,  and  time. 

2.  At  what  distance  must  a  small  sphere  charged  with  28 
units  of  electricity  be  placed  from  a  second  sphere  charged  with 
56  units  in  order  to  repel  the  latter  with  a  force  of  32  dynes?   - 

Ans.   7  centimetres. 

3.  Suppose  the  distance  from  the  earth  to  the  moon  to  be  (in 
round  numbers)  383  x  io8  centimetres  ;  and  that  the  radius  o/ 
the  earth  is  63  x  ior  centimetres,  and  that  of  the  moon  15  x 
io7' centimetres  ;  and  that  both  moon  and  earth  ^are  charged 
until  the  surface  density  on  each  of  them  is  of  the  average  value 
of  io  units  per^square  centimetre.     Calculate  the  'electrostatic- 
repulsion  between  the  moon  and  the  earth, 

4.  A  small  sphere  is  electrified  with  24  units  of  +  electricity. 
Calculate  the  force  with  which  it  repels  a  unit  of  +  electricity  at 
distances  of  I,  2,  3,  4,  5,  "5,  8,  and  io  centimetres  respectively. 
Then  plot  out  the  "curve  of  force"  to  scale;  measuring  the 
respective,  distances  along  a  line  from  left  to  right  as  so  many 
centimetres  from  a  fixed  point  as  origin ;  then  setting  p>U  as 


428  PROBLEMS  AND  EXERCISES. 

vertical  ordinates  the  amounts  you  have  calculated  for  the 
corresponding  forces ;  lastly,  connecting  by  a  curved  line  the 
system  of  points  thus  found. 

5  Define  electrostatic  (or  electric)  "potential ;"  and  calculate 
(by  the  rule  given  in  italics  in  Art.  238)  the  potential  at  a  point 
A,  which  is  at  one  corner  of  a  square  of  8  centimetres'  side, 
when  at  the  other  three  corners  B,  C,  D,  taken  in  order, 
charges  of  +  16,  +34,  and  +  24  units  are  respectively  placed. 

Ans.   8,  very  nearly  exactly, 

6,  A  small  sphere  is  electrified  with  24  units  of  +  electricity. 
Calculate  the  potential  due  to  this  charge  at  points  I,  2,  3,  4,  5, 
6,  8,  and  10  centimetres'  distance  respectively.     Then  plot  out 
the  "curve  of  potential"  to  scale,  as  described  in  Question  4. 

7,  What  are  equipotential  surfaces  ?     Why  is  the  surface  of 
an  insulated  conductor  an  equipotential  surface  ?    Is  it  always 
so? 

8.  A  sphere  whose  radius  is  14  centimetres  is  charged  until 
the   surface  density  has  a  value   of  10.      What  quantity  of 
electricity  is  required  for  this  ?          Ans.  24, 640  units  (nearly). 

9.  In  the  above  question  what  will  be  the  potential  at  the 
surface  of  the  sphere?    (See  last  sentence  of  Art.  246.) 

Ans»   1760  (very  nearly). 

to.  In  the  case  of  question  8,  what  will  be  the  electric  force  at 
a  point  outside  the  sphere  and  indefinitely  near  to  its  surface  ? 
(Art.  251.)  Ans.  1257  (very  nearly). 

n.  Suppose  a  sphere  whose  radius  is  10  centimetres  to  be 
charged  with  6284  units  of  electricity,  and  that  it  is  then  caused 
to  share  its  charge  with  a  non-electrified  sphere  whose  radius  is 
15  centimetres,  what  will  the  respective  charges  and  surface - 
densities  on  the  two  spheres  be  when  separated  ? 

Ans.  Small  sphere,  q  —  2513-6,  j»  =  a  : 
Large  sphere,  q  =  3770-4,  S  =  1  '33- 

12.  A  charge  of  +  8  units  is  collected  at  a  point  20  centi- 
metres distant  from  the  centre  of  a  metallic  sphere  whose  radius 
is  10  centimetres.  It  induces  a  negative  electrification  at  the 
nearest  side  of  the  sphere.  Find  a  point  inside  the  sphere  such 
that  if  4  negative  units  were  placed  there  they  would  exercise 


PROBLEMS  AND  EXERCISES.  429 


a  potential  on  all  external  points  exactly  equal  to  that  of  ths 
actual  negative  electrification.     (See  Art.  250.) 

Ans.  The  point  must  be  on  the  line  between  the  outside 

positive  charge  and  the  centre  of  the  sphere  and  at 

5  centims.  from  the  surface. 

13.  Two  large  parallel  metal  plates  are  charged  both 
positiyely  but  unequally,  the  density  at  the  surface  of  A  being 
+  6,  that  at  the  surface  of  B  being  +  3.  They  are  placed  2 
centimetres  apart.  •  Find  the  force  with  which  a  +  unit  of 
electricity  is  urged  from  A  towards  B.  Find  also  the  work 
done  by  a  +  unit  of  electricity  in  passing  from  A  to  B. 

Ans.  Electric  force  from  A  towards  B  =  1 8  '85  dynes;  work 
done  by  unit  in  passing  from  A  to  B  =  37-5  ergs. 

.  14.  What  is  meant  by  the  dimensions  of  a  physical  quantity  ? 
Deduce  from  the  Law  of  Inverse  Squares  the  dimensions  of 
electricity  j  and  show  by  this  means  that  electricity  is  not  a 
quantity  of  the  same  physical  dimensions  as  either  matter ;  energy, 
or  force. 

15.  Explain  the  construction  and  principles  of  action  of  the 
quadrant  electrometer.     How  could  this  instrument  be  made 
self-recording  ? 

1 6.  One  of  the  two  coatings  of  a  condenser  is  put  to  earth, 
to  the  other  coating  a  charge  of  5400  units  is  imparted.     It  is 
found  that  the  difference  of  potential  thereby  produced  between 
the  coatings  is  15  (electrostatic)  units.     What  was  the  capacity 
©f  the  condenser  ?  Ans.    360. 

17.  What  is  the  meaning  of  specific  inductive  capacity!    Why 
does  hot  glass  appear  to  have  a  higher  specific  inductive  capacity 
than  cold  glass  ? 

1 8.  Compare  the  phenomenon  of  the  residual  charge  in  a 
Leyden  jar  with  the  phenomenon  of  polarisation  in  an  electro- 
lytic cell. 

19.  A  condenser  was  made  of  two  flat  square  metal  plates,, 
the  side  of  each  of  them  being  35  centimetres.     A  sheet  of 
tndiarubber  '4  centim.   thick  was  placed  between  them  as  a 
dielectric.      The    specific    inductive    capacity   of    indiarubber 

taken  as  2-25,  calculate  the  capacity  of  the  condenser. 

Ans.  548-8  electrostatic  units. 


430  PROBLEMS  AND  EXERCISES. 

20.  Calculate  (in  electrostatic  units)  the  capacity  of  a  mile  of 
telegraph  cable  the  core  being  a  copper  wire  of  -18  centim. 
diameter,  surrounded  by  a  sheathing  of  guttapercha  -91  centim. 
thick.      \k    for    guttapercha   =   2-46;    one    mile  =  160,933 
centims.]  Ans.  Sc  164  units. 

21.  A  Leyden  jar  is  made  to  share  its  charge  with  two  other 
jars,  each  of  which  is  equal  to  it  in  capacity.     Compare  the 
energy  of  the  charge  in  one  jar  with  the  energy  of  the  original 
charge.  ^ns'   ^ne  mnt^  as  great. 


22.  A  series  of  Leyden  jars  of  equal  capacity  are  charged 
"in  cascade."     Compare  the  total  energy  of  the  charge  of  the 
individual  jars  thus  charged,  with  that  of  a  single  jar  charged 
from  the  same  source. 

23.  Classify  the  various  modes  of  discharge,  and  state  the 
conditions  under  which  they  occur. 

24.  Suppose  a  condenser,  whose  capacity  is  10,000  charged 
to  potential  14,  to  be  partially  discharged  so  that  the  poiential 
fell   to    5.     Calculate   the   amount    of  heat   produced  by  the 
discharge,  on  the  supposition  that  all  the  energy  of  the  spark 
is  converted  into  heat."  Ans.    -020357  of  a  unit  of  heat. 

25.  riow  do  changes  of  pressure  affect  the  passage  of  eieclric 
sparks  through  air  ? 

26.  Why  are  telegraphic  signals  through  a  submerged  cable 
retarded    in    transmission,    arid    how    can    this  recardation  be 
obviated  ? 

27.  How  is  the  difference  of  potential  between  the  earth  and 
the  air  above  i'.  measured  ?  and  what  light  do  such  measure- 
ments throw  on  the  periodic  variations  in  the  eleclrical  state  ol 
the  atmosphere  ? 

28.  What  explanation  can  be  given  o/  the  phenomena  of  a 
thunderstorm  ? 

29.  What  are  the  essential  features  which  a  lightning-con- 
ductor mist  possess  before  it  can  be  pronounced  satisfactory? 
And  what  are  the  reasons  for  insisting  on  these  points  ? 

30.  How  can  the  duration  of  an  electric  spark  be  measured  ? 


PROBLEMS  AND  EXERCISES.  431 


QUESTIONS  ON  CHAPTER  V. 

1.  Define  magnetic  potential,  and  find  the  (magnetic)  potential 
due  to  a  bar  magnet  10  centimetres  long,  and  of  strength  So, 
at  a  point  lying  in  a  line  with  the  magnet  poles  and  6  centi- 
metres distant  from  its  N.  -seeking  end.  Ans.   8-3. 

2.  A  N. -seeking  pole  and  a  S. -seeking  pole,  whose  strengths 
are  respectively  +  120  and  —  60,  are  in  a  plane  at  a  distance 
of  6  centimetres  apart.      Find  the  point  between  them  where 
the  potential  is  =  o  ;  and  through  this  point  draw  the  curve  of 
zero  potential  in  the  plane. 

3.  Define    "intensity   of  the    magnetic    field."     A  magnet 
whose  strength  is  270  is  placed  in  a  uniform  magnetic   field 

whose  intensity  is  'i66.     What  are  the  forces  which  act  upon 
its  poles  ?  Ans.  +  45  dynes  and  —  45  dynes. 

4.  Define  "intensity  of  magnetisation."     A  rectangular  bar- 
magnet,  whose  length  was  9  centimetres,  was  magnetised  until 
the  strength  of  its  poles  was  164.     It  was  2  centimetres  broad 
and  '5  centimetre  thick.      Supposing  it  to  be  uniformly  magnet- 
ised throughout  its  length,  what  is  the  intensity  of  the  magnet- 
isation? A  us.    164. 

5.  Poisson  suggested  a  two -fluid  theory  of  magnetism,  the 
chief  point  of  the  hypothesis  being  that  in  the  molecules  of  iron 
and  other  magnetic  substances  there  were  equal  quantities  of 
two  opposite  kinds  of  magnetic  fluid  ;  and  that  in  the  act  of 
magnetisation  the  two  fluids  were  separated.     What  facts  does 
this  theory  explain  ?     What  facts  does  it  fail  to  explain  ? 

6.  A  current  whose  strength  in  "  absolute  "  electromagnetic 
units  was  equal  to  0-05  traversed  a  wire  ring  of  2  centimetres 
radius.     What  was  the  strength  of  field  at  the  centre  of  the 
ring?     What  was   the    potential  at   a   point    P    opposite   the 
middle  of  the  ring  and  4  centimetres  distant  from  the  circum- 
ference of  the  ring.  Ans.  f—  '1571 ;  V  =  ±    0*0421. 

7.  What  limits  are  there  to  the  power  of  an  electromagnet  ? 

8.  What  is  %  the  advantage  of  tho  iron  core  in  an  electro- 
magnet ? 

9.  Assuming  the  effective  coefficient  oi  magnetisation  of  iron 


432  PROBLEMS  AND  EXERCISES. 

to  be  20,  calculate  the  strength  of  the  pole  of  an  electromagnet 
whose  coils  consist  of  50  turns  of  wire  of  an  average  radius  of 
I  centimetre,  when  a  current  of  -2  amperes  passes  through  the 
coils,  the  core  consisting  of  a  bar  5  centimetres  long  and  of  I 
square  centimetre  of  area  in  its  cross  section  [see  Art.  328]. 

Ans,  528  units. 

10.  Enunciate  Maxwell's  rule  concerning   magnetic   shells, 
and  from  it  deduce  the  laws  of  parallel  and  oblique  currents 
discovered  by  Ampere. 

11.  A  circular  copper  dish  is  joined  to  the  zinc  pole  of  a 
small  battery.     Acidulated  water  is  then  poured  into  the  dish, 
and  a  wire  from  the  carbon  pole  of  the  battery  dips  into  the 
liquid  at  the  middle,      A  few  scraps  of  cork  are  thrown  in  tc 
render  any  movement  of  the  liquid  visible.     What  will  occur 
when  the  N. -seeking  pole  of  a  strong  bar-magnet  is  held  above 
the  dish  ? 

1 2.  Roget  hung  up  a  spiral  of  copper  wire  so  that  the  lower 
end  just  dipped  into  a  cup  of  mercury.     When  a  strong  current 
was  sent  through  the  spiral  it  started  a  continuous  dance,  the 
lower  end  producing  bright  sparks  as  it  dipped  in  and  out  of 
the  mercury.     Explain  this  experiment. 

13.  It  is  believed,  though  it  has  not  yet  been  proved,  that 
ozone  is  more  strongly  magnetic  than  oxygen.     How  could  this 
be  put  to  proof? 


QUESTIONS  ON  CHAPTER  VI. 

1.  The  resistance  of  telegraph  wire  being  taken  as  13  ohms, 
per  mile,  and  the  E.  M.  F.  of  a  Leclanche  cell  as  1-5  volt^ 
calculate  how  many  cells  are  needed  to  send  a  current  of  12 
milli-amplres  through  a  line  120  miles  long  ;  assuming  that  the 
instruments  in  circuit  offer  as  much  resistance  as  20  miles  of 
wire  would  do,  and  that  the  return-current  through  earth  meets 
with  no  appreciable  resistance.  Ans.   \  5  cells. 

2.  50  Grove's  cells  (E.   M.   F.   of  a  Grove  =  I  8  volt)  are 
united  in  series,  and  the  circuit  is  completed  by  a  wire  whose 
resistance  is  1 5  ohms.     Supposing  the  internal  resistance  of  each 
cell  to  be  0-3  ohm>  calculate  the  strength  of  the  current 

Ans.  3  ampfrn. 


PROBLEMS  AND  EXERCISES.  433 

3.  The  current  running  through  an  incandescent  filament  of 
carbon  in   a  lamp   was  found   to  be   exactly   I  ampere.     The 
difference  of  potential  between  the  two  terminals  of  the  lamp 
while  the  current  was  flowing  was  found  to  be  30  volts.     What 
was  the  resistance  of  the  filament  ? 

4.  Define  specific  resistance.     Taking  the  specific  .resistance 
of  copper  as'  1642,  calculate  the  resistance  of  a  kilometre  of 
copper  wire  whose  diameter  is  I  millimetre.      Ans.   20*9  ohms. 

5.  On  measuring  the  resistance  of  a  piece  of  No.  30  B.  W.  G. 
(covered)  copper  wire,  18*12  yards  long,  I  found  it  to  have  a 
resistance  of  3  -02  ohms.   Another  coil  of  the  same  wire  had  a  resist- 
ance of  22*65  ohms  ;  what  length  of  wire  was  there  in  the  coil  ? 

Ans.    135*9  yards. 

6.  Calculate  the  resistance  ot  a  copper  conductor  one  square 
centimetre  in  area  of  cross-section,. and  long  enough  to  reach 
from   Niagara  to  New  York,   reckoning  this  distance  as  480 
kilometres.  Ans.   78*8  ohms. 

7.  You  have  given  an  unlimited  number  of  Telegraph  Daniell's 
cells  (Fig.  77),  their  E.  M.  F.  being   IT  volt  each,  and  their 
average  internal  resistance  being  2 '2  ohms  each.     What  will  be 
the  strength  of  the  current  when  five  such  cells,  in  series,  are 
connected  through  a  wire  whose  resistance  is  44  ohms  t 

Ans.  O'l  amptre. 

8.  Show  in  the  preceding  case  that  with  an  infinite  number 
of  cells  in  scries,  the  current  could  not  possibly   exceed  0*5 
ampere. 

9.  The  specific  resistance  of  guttapercha  being  3*5  x   xo23, 
calculate  the  number  of  coulombs  of  electricity  that  would  leak 
in  one  century  through  a  sheet  of  guttapercha  one  centimetre 
thick  and  one    metre  square,  whose  faces  were    covered  with 
tinfoil  and  joined  respectively  to  the  poles  of  a  battery  of  100 
Daniell's  cells.  Ans.   9*7  coulomb. 

10.  Six  Daniell's  cells,  for  each  of  which  E  =  1-05  volts,  r= 
0*5  ohm,  are  joined  in  series.     Three  wires,  X,Y,  and  Z,  whose 
resistances  are  severally  3,  30,  and  300  ohms,  can  be  inserted 
between  the  poles  of  the  battery.     Determine  the  current  (in 
amperes)  which  flows  when  each  wire  is  inserted  separately  ;  also 
determine  that  which  flows  when  they  are  all  inserted  at  once 
in  parallel  arc. 


PROBLEMS  AND  EXERCISES. 


Ans.   Through  X  I  -05      amperes  per  sec. 

Through  Y  0-1909        „  „ 

Through  Z  0*0207        »  i» 

Through  all  three  1-105          »»  » 

1  1.  Calculate  the  number  of  cells  required  to  produce  a 
current  of  50  milli-amptres,  through  a  line  114  miles  long,  whose 
resistance  is  12^  ohms  per  mile,  the  available  cells  of  the  battery 
naving  each  an  internal  resistance  of  i'5  ohm,  and  an  E.M.F.  of 
i  -5  volt.  Ans.  50  cells. 

12.  You  have  20  large  Leclanche  cells  (E.M.F.  =  1*5  volt, 
/•=O'5  oh»t  each)  in  a  circuit  in  which  the  external  resistance  is 
10  ohms.     Find  the  strength  of  current  which  flows  (a)  when 
the  cells  are  joined  in  simple  series  ;  (b)  all  the  zincs  are  united, 
and  all  the  carbons  united,  in  parallel  arc  ;  (c)  when  the  cells  are 
arranged  two  abreast  (i.e.  in  two  files  of  ten  cells  each)  ;  (d) 
•when  the  cells  are  arranged  four  abreast. 

Ans.   (a)  1*5         amptre. 
(b)  0-1496      „ 

(f)  i'2 

(d)  0702       „ 

13.  With  the  same  battery  how  would  you  arrange  the  cells 
in  order  to  telegraph  through  a  line   100  miles  long,  reckoning 
the  line  resistance  as  12^  ohms  per  mile? 

14.  I  have  48  cells,  each  of  1-2  volt  E.M.F.,  and  each  of 
2  ohms  internal  resistance.     What  is  the  best  way  of  grouping 
them  together  when  it  is  desired  to  send  the  strongest  possible 
current  through  a  circuit  whose  resistance  is  12  ohms? 

Ans.  Group  them  three  abreast. 

15.  Show  that,  if  we  have  a  battery  of  n  given  cells  each  of 
resistance  r  in  a  circuit  where  the  external  resistance  is  R,  the 
strength  of  the  current  will  be  a  maximum  when  the  cells  arc 
coupled  up  in  a  certain  number  of  rows  equal  numerically  tc 

V  "wr-5-R. 

1  6.  Two  wires,  whose  separate  resistances  are  28  and  24,  are 
placed  in  parallel  arc  in  a  circuit  so  that  the  current  divides, 
part  passing  through  one,  part  through  the  other.  What  resist- 
ance do  they  offer  thus  to  the  current  ?  Ans.  12  '92  ohms. 

17.  Using  a  large  bichromate  cell  of  practically  no  internal 
resistance,  a  deflection  of  9°  was  obtained  upon  a  tangent 


PROBLEMS  AND  EXERCISES. 


435 


galvanometer  (also  of  small  resistance)  through  a  wire  whose 
resistance  was  known  to  be  435  ohms.  The  same  cell  gave  a 
deflection  of  5°  upon  the  same  galvanometer  when  a  wire  of 
unknown  resistance  was  substituted  in  the  circuit.  What  was 
the  unknown  resistance  ?  Ans.  790  ohms. 

1 8.  In  a  Wheatstone's  bridge  in  which  resistances  of  10  and 
loo  ohms  respectively  were  used  as  the  fixed  resistances,  a  wire 
whose  resistance  was  to  be  determined  was  placed  :  its  resist- 
ance was  balanced  when  the  adjustable  coils  were  arranged  to 
throw  28 1  ohms  into  circuit.     What  was  its  resistance  ? 

Ans.   28*1  ohms. 

19.  A  battery  of  5  Leclanche  cells  was  connected  hi  simple 
circuit  with  a  galvanometer  and  a  box  of  resistance  coils.     A 
deflection  of  40°  kaving  been  obtained  by  adjuctinent  of  the 
resistances,  it  was  found  that  the  introduction  of  150  additional 
ohms  of  resistance  brought  doWn  the  deflection  to  29°.    A  battery 
of  ten  Danieil's  cells  was  then  substituted  in  the   circuit  and 
adjusted  until  the  deflexion  was  40°  as  before.     But  this  time  it 
was  found  that  2 1 6  ohms  had  to  be  added  before  the  .deflection 
was  brought  down  to  29°.     Taking  the  E.M.F.  of  a  single 
Danieil's  cell  as  I  '079  volt,  calculate  that  of  a  single  Leclanche 
ce'  Ans.   I  '499  volt. 

20.  How   are   standard    resistance  coils  wound,   and  why? 
What  materials  are  they  made  of,  and  why  ? 

21.  Three  very  small  Danieil's  cells  gave,  with  a  sine  galvan- 
ometer (itself  of  no  appreciable  resis'ance),  a  reading  of  57°«    On 
throwing  20  ohms  into  the  circtu:  the  galvanometer  reading  fell 
to  25°.     Calculate  the  internal  resistance  of  the  cells. 

Ans.  6*6  ohms  each. 

22.  A  knot  of  telegraph  cable  was  plunged  in  a  tub  of  water 
and  then  charged  for  a  minute  from  a  battery  of  120  Danieil's 
cells.      The   cable  was   then  discharged   through    a  long -coil 
galvanometer  with  a  needle  of  slow  swing.     The  first  swiug 
was  40°.     A  condenser  whose  capacity  was  \  microfarad  was 
then  similarly  charged  and  discharged  ;  but  this  time  the  first 
swing  of  the  needle  was  only  over  14°.     What  was  the  capacity 
of  the  piece  of  cable  ?  Ans.  0-934  microfarad. 

23.  Usinj  en  absdutc  electrometer,  Sir  W.  Thomson  found 
the  difference  of  potential  between  the  poles  of  a  Danieil's  cell 


436  PROBLEMS  AND  EXERCISES. 

to  be  '00374  electrostatic  units  (C.G.S.  system).  The  ratio  of 
the  electrostatic  to  the  electromagnetic  unit  of  potential  is  given 

in  Art.  365,  being  =  *.  The  volt  is  defined  as  io8  electromag- 
netic units.  From  these  data  calculate  the  E.  M.  F.  of  a 
Darnell's  cell  in  volts.  Ans,  1*115  w& 

24.  The  radius  of  the  earth  is  approximately  63  x  io7  centi- 
metres.    The  ratio  of  the  electrostatic  to  the  electromagnetic 
unit  of  capacity  is  given  in  Art.  365.     The  definition  of  the 
farad  is  given  in  Art.  323.     Calculate  the  capacity  of  the  earth 
(regarded  as  a  sphere)  in  microfarads. 

Ans.   7°°  microfarads  (nearly). 

25.  The  electromotive-force  of  a  Daniell's  cell  was  determined 
by  the  following  process : — Five  newly-prepared  cells  were  set 
up  in  series  with  a  tangent  galvanome'ter,  whose  constants  were 
found  by  measurement.     The  resistances  of  the  circuit  were  also 
measured,  and  found  to  be  in  total  16-9  ohms.     Knowing  the 
resistance  and  the  absolute  strength  of  current  the  E.M.F.  could 
be  calculated.     The  deflection  obtained  was  45°,  the  number  of 
turns  of  wire  in  the  coil  io,  the  average  radius  of  the  coils  II 
centimetres,  and  the  value  of  the  horizontal  component  of  the 
earth's  magnetism  at  the  place  was  O'i8  C.G.S.  units.     Deduce 
the  E.M.F.  of  a  Daniell's  cell. 

Ans.    i -0647  x  io8  C.G.S.  units,  or  1*0647  v°lt* 


QUESTIONS  ON  CHAPTER  VII. 

1.  I  have  seen  a  small  chain  in  which  the  alternate  links 
were  of  platinum  and  silver  wires.     When  an  electric  current 
was  sent  through  the  chain  the  platinum  links  grew  red  hot 
while  the  silver  links  remained  cold.     Why  was  this  ? 

2.  Calculate  by  Joule's  law  the  number  of  heat  units  developed 
in  a  wire  whose  resistance  is  4  ohms  when  a  steady  current  of 
•14  amptre  is  passed  through  it  for  io  minutes. 

Ans.  '\  I  '2  units  of  heat. 

3.  What  sort  of  cells  ought   to   be  the  best  for  providing 
currents  to  fire  torpedo  shots  ? 

4.  Explain  why  a  regulator  like  that  of  Duboscq  is  employed 
in  obtaining  a  steady  voltaic  arc. 


PROBLEMS  AND  EXERCISES.  437 

5.  I  once  tried  to  obtain  an  electric  light  by  using  a  battery 
of  3000  telegraph  Daniell's  cells  in  series,  but  without  success, 
Why  did  this  enormous  battery  power  fail  for  this  purpose? 
Could  it  have  been  made  to  give  a  light  by  any  different  arrange- 
ment of  the  cells  ? 

6.  A  battery  of  2  Grove's  cells,  a  galvanometer,  and  a  little 
electromagnetic  engine,  were  connected  in  circuit.     At  first  the 
engine  was  loaded,  so  that  it  could  only  run  slowly  ;  but  when 
the  load  was  lightened  it  spun  round  at  a  tremendous  speed. 
But   the   faster   the  little   engine  worked   the  feebler  was  the 
current  indicated  by  the  galvanometer.     Explain  this. 

7.  A  purrent  of  9  amperes  worked  an  electric  arc  light,  and  on 
measuring  the  difference  of  potential  between  the  two  carbons 
by  an  electrometer  it  was  found  to  be   140  volts.     What  was 
the  amount  of  horse-power  absorbed  in  this  lamp  ? 

Ans.  1-69  H.-P. 

8.  You  have  a  lathe  in  your  workshop  which  requires  power 
to  turn  it.     There  is  a  stream  of  water  tumbling  down  the  hill- 
side, two  miles  off,  with  power  enough  to  turn  twenty  lathes. 
How  can  you  bring  this  power  to  the  place  where  you  want  to 
use  it  ? 

9.  What  5s  the   use  of  the  electro-dynamometer  ?     Assum- 
ing that  the  moment  of  the  force  acting  on  the  movable  coil  of 
the  electro-dynamometer  is  proportional  to  the-  product  of  the 
strengths  of  the  currents  in  the  two  coils,  show  that  the  work 
performed    by   a   current   is    really    measured   by  the  electro- 
dynamometer  of  Marcel  Deprez,  in  which  one  set  of  coils  has  a 
very  small  resistance  and  the  other  a  very  high  resistance  (con- 
sisting of  many  turns  of  fine  wire),  the  latter  being  arranged  as 
a  shunt  to  the  lamp,  motor,  or  other  instrument,  in  which  the 
work  to  be  measured  is  being  done,   the  former  having   the 
whole  current  passed  through  it. 


QUESTIONS  ON  CHAPTER  VIII. 

I.  A  strong  battery -current  is  sent,  for  a  few  moments, 
through  a  bar  made  of  a  piece  of  antimony  soldered  to  a  piece 
of  bismuth.  The  battery  is  then  disconnected  from  the  wires 
and  they  are  joined  to  a  galvanometer  which  shows  a  deflection. 
Explain  this  phenomenon. 


438  PROBLEMS  AND  EXERCISES. 


2.  A  long  strip  or  zinc  is  connected  to  a  galvanometer  by 
iron  wires.     One  junction  is  kept  in  ice,  the  other  is  plunged 
into  water  of  a  temperature  of  5o°C.     Calculate,  from  the  table 
given  in  Art.  381,  the  electromotive-force  which  is  producing 
the  current.  Ans,  690  microvolts. 

3.  When  heat  is  evolved  at  a  junction  of  two  metals  by  the 
passage  of  a  current,  how  would  you  distinguish  between  the 
heat  due  to  resistance  and  the  heat  due  to  the  Peltier  effect  ? 

4.  Sir  W.  Thomson  discovered  that  when  a  current  flows 
through  iron  it  absorbs  heat  when  it  flows  from  a  hot  point 
to  a  cold  point ;  but  that  when  a  current  is  flowing  through 
copper  it  absorbs  heat  when  it  flows  from  a  cold  point  to  a  hot 
point.     From  these  two  facts,  and  from  the  general  law  that 
energy  tends  to  run  down  to  a  minimum,  deduce  which  way  a 
current  will  flow  round  a  circuit  made  of  two  half-rings  of  iron 
and  copper,  one  junction  of  which  is  heated  in  hot  water  and  the 
other  cooled  in  ice. 


QUESTIONS  ON  CHAPTER  IX. 

1 .  Give  the  reasons  which  exist  for  thinking  that  light  is  an 
electromagnetic  phenomenon., 

2.  How  is  the  action  of  magnetic  forces  upon  the  directioc 
of  the  vibrations  of  light  shown?  and  what  is  the  difference 
between  magnetic  and  diamagnetic  media  in  respect  of  theii 
magneto-optic  properties  ? 

3.  It  was  discovered  by  Willoughby  Smith  that  Jhe  resistance 
of  selenium  is  less  when  exposed  to  light  than  in  the  dark. 
Describe  the  apparatus  you  would  employ  to  investigate  this 
phenomenon.     How  would  you  proceed  to  experiment  if  you 
wished  to  ascertain  whether  the  amount  of  electric  effect  was 
proportional  to  the  amount  of  illumination  ? 


QUESTIONS  ON  CHAPTER  X. 

l.  The  ends  of  a  coil  of  fine  insulated  wire  are  connected 
with  terminals  of  a  long-coil  galvanometer.     A  steel  bar-magnel 


PROBLEMS  AND  EXERCISES.  439 

i<5  placed  slowly  into  the  hollow  of  the  coil,  and  then  witndrawn 
suddenly.  What  actions  will  be  observed  on  the  needle  of  the 
galvanometer  ? 

2.  Round  the  outside  of  a  deep  cylindrical  jar  are  coiled  two 
separate  pieces  of  fine  silk -covered  wire,  each  consisting  of  many 
;ums.     The  ends  of  one  coil  are  fastened  to  a  battery,  those  of 
the  other  to  a  sensitive  galvanometer.     When  an  iron  bar  is 
poked    into    the  jar   a  momentary  current  is  observed  in  the 
galvanometer  coils,  and  when  it  is  drawn  out  another  moment- 
ary current,  but  in  an  opposite  direction,  is  observed.     Explain 
these  observations. 

3.  A  casement  window  has  an  iron  frame.     The  aspect  is 
north,  the  hinges  being  on  the  east  side.     What  happens  when 
the  window  is  opened? 

4.  Explain  the  construction  of   the    induction-coil.     What 
are  the  particular  uses  of  the  condenser,   the  automatic  break, 
and  the  iron  wire  core  ? 

5.  It  is  desired  to' measure  the  strength  of  the  field  between 
the  poles  of  an  electromagnet  which  is  excited  by  a  current  from 
a  constant  source.     How  could  you  apply  Faraday's  discovery 
of  induction  currents  to  this  purpose  ? 

6.  What  is  meant  by  the  term  "extra-currents?"'     A  small 
battery  was  joined  in  circuit  with  a  coil  of  fine  wire<and  a 
galvanometer,   in  which   the   current  -was  found  to  produce  a 
steady  but  small  deflection.    ,An  unmagnetised  iron  bar  was 
now  plunged  into  the  hollow  of  the  coil  and  then  withdrawn. 
The  galvanometer  needle  was  observed  to  recede  momentarily 
from  its  first  position,  then  to  -return  and  to  swing  beyond  it 
with  a  wider  arc  than  before,  and  finally  to  settle  down  to  its 
original  deflection.     Explain  these  actions. 

7.  In  what  respect  do  dynamo -electric  machines  differ  from 
magneto-electric  machines  ?     Where  does  the  magnetism  of  the 
field -magnets   come   from   in    the   former?     Where  does  the 
dynamical  energy  of  the  currents  come  from  in  the  latter  ? 

8.  The    older    magneto -electric    machines   produced   only 
intermittent   currents,    and  'these    were   usually  alternating  in 
direction.     By  what  means  .do  the  more  modern  magneto-electric 
generators  produce  currents  which 'are  continuous  and  direct! 


440  PROBLEMS  AND  EXERCISES. 

9.  A   compass   needle,    when    set    swinging,   comes  to  rest 
sooner  if  a  plate  of  copper  is  placed  beneath  it  than  if  a  plate  of 
glass  or  wood  lies  beneath  it.     Explain  this  fact. 

10.  Explain   how  it  is  that  on  making  circuit    the   current 
rises  only  gradually  to  its  full  strength,  especially  if  there  are 
large  electromagnets  in  the  circuit. 

1 1 .  Foucault  set  the  heavy  bronze  wheel  of  his  gyroscope 
spinning  between  the  poles  of  a  powerful  electromagnet,  an<l 
found  that  the  wheel  grew  hot,  and  stopped.     What  was  the 
cause  of  this  ?     Where  did  the  heat  come  from  ? 

12.  The  strength  of  the  field  between  the  poles  or'  a  laige 
electromagnet   was   determined   by   the  following  means  :  —  A 
small  circular  coil,  consisting  of  40  turns"  of  fine  insulated  wire, 
mounted  on  a  handle,  was  connected  to  the  terminals  of  a  long- 
coil  galvanometer  having  a  heavy  needle.     On  inverting  this  coil 
suddenly,  at  a  place  where  the  total  intensity  of  the  earth's  mag- 
netic force  was  '48  unit,  a  deflection  of  6°  vas  shown  as  the  first 
swing  ,of  the   galvanometer  needle.     The   sensitiveness  of  the 
galvanometer  was  then  reduced  to  -rH  by  means  of  a  shunt.    The 
little  coil  was  introduced  between  the  poles  of  the  electromagnet 
and  suddenly  inverted,    when   the  first  swing  of  the   galvan- 
ometer needle  reached  40°.     What  was  the  strengih  of  the  field 
between  the  pol***?  Ans,  315*7  "nits. 


QUESTIONS  ON  CHAPTER  XI. 

1.  It  is  found  that  a  single  Daniell's  cell  will  not  electiolyse 
acidulated  water,  however  big  it  may  be  made.      It  is -found,  on 
the  other  hand,  that   two. Daniell's  cells,   however  small,  will 
suffice  to  produce  continuous  electrolysis  of  acidulated  water. 
How  do  you  account  for  this? 

2.  When  a  gramme  of  zinc  combines  with  oxygen  it  gives 
out    1301    heat-units.     When  this  zinc  oxide   is  dissolved    in 
sulphuric  acid  369  more  units  are  evolved.     To  separate   an 
equivalent  amount  of  copper  sulphate  into  sulphuric  acid  and 
copper  oxide  requires    588    heat -units   to   be   expended.     To 
separate  the  copper  from  the  oxygen  in  this  oxide  requires  293 
more  heat^units.     The  absolute  electro -chemical  equivalent  of 
tine  is  0-00341 2  (see  Art.  212),  and  Joule's  dynamical  equivalent 


PROBLEMS  AND  EXERCISES.  441 

« 

of  heat  is  42  x  io6.     From  these  figures  calculate  the  electro- 
motive foice  of  a  Daniell's  cell. 

Ans.  rno6  x  io3  C.G.S.  units,  or 
1.1306.  volt, 

3.  Explain  the  operation  of  charging  a  secondary  battery. 
What  are  the  chemical  actions  which  go  on  during  charging  and 
during  discharging  ? 

4.  Most   liquids  which  conduce    electricity  are  decomposed 
(except  the  melted  metals)  in  the  act' of  conducting.     How  do 
you  account  for  the   fact  observed   by  Faiaday  that  the  amount 
of  matter  transfeiied  through  the  liquid  and  deposited  on  the 
electrodes  is  pioportional  to  the  amount  of  electricity  trans- 
ferred through  the  liquid  ? 

5.  Describe  the  process  for  multiplying  by  electricity  copies 
of  engravings  on  wood-blocks. 

6.  How  would  you  make  arrangements  for  silvering  spoons 
of  nickel-bronze  by  electio-deposition? 

QUESTIONS  ON  CHAPTER  XII. 

1.  Sketch  an  airangemeut  by  •which  a  single  line  of  wire  can 
be  used  by  an  operator  at  either  end  to  signal  to  the  other ;  the 
con-lition  of  working  being  that  whenever,  you  are  not  sending 
a  message  yourself  your  instrument  shall  be  in  circuit  with  the 
line  wire,  and  out  <?/"cucuit  uith  the  battery  at  your  own  end. 

2.  \Ylxat   advantages  has   the    Morse   instrument   over   the 
needle  instruments  intioduced  into  telegraphy  by  Cooke  and 
Wheatstone  ? 

3.  Explain  the  use  and  construction  of  a  relay. 

4.  It  is  desirable  in  certain   cases  (diplex  and    quadruples 
signalling)  to  arrange  telegraphic  instruments  so  that  they  will 
respond  only  to  currents  which  come  in  one  direction  through 
the  line.     Haw  can  this  be  done  ? 

5.  A  battery  is  set  up  at  one  station.     A  galvanometer  needle 
at  a  station  eighty  miles  away  is  deflected  through  a  certain 
number  of  degiees  when  the  wire  of  its  coil  makes  twelve  turns 
round  the   needle  ;    wire  of  the  same  quality  being  used  for 
both  line  and  galvanometer.     At  200  miles  the  same  deflection 
is  obtained  when  twenty -four  turns  are  used  in  the  galvan- 

2  G 


442  PROBLEMS  AND  EXERCISES. 

ometer-coil.  Show  by  calculation  (a)  that  the  internal  resist- 
ance of  the  battery  is  equal  to  that  of  40  miles  of  the  line-wire  ; 
(b)  that  to  produce  an  equal  deflection  at  a  station  360  miles 
distant  the  number  of  turns  of  wire  in  the  galvanometer -coil 
must  be  40. 

6.  Suppose  an  Atlantic  cable  to  snap  off  short  during  the 
process  of  laying.     How  can  the  distance  of  the  broken  end 
from  the  shore  end  be  ascertained  ? 

7.  Suppose  the  copper  core  of  a  submarine  cable  to  part  at 
some  point  in  the  middle  without  any  damage  being  done  to 
the  outer  sheath  of  guttapercha.     How  could  the  position  of 
the  fault  be  ascertained  by  tests  made  at  the  shore  end  ? 

8.  Explain  the  construction  and  action  of  an  electric  bell. 

9.  Describe  and  explain  how  electric  currents  are  applied  in 
the   instruments   by   which    very   short  intervals   of  time   are 
measured. 

10.  Explain   the   use   of  Graham    Bell's   telephone    (i)    to 
transmit  vibrations  ;  (2)  to  reproduce  vibrations. 

11.  Describe  a  form  of  telephone  in  which  the  vibrations  of 
sound  are  transmitted  by  means  of  the  changes  they  produce  in 
the  resistance  of  a  circuit  in  which  there  is  a  constant  electro- 
motive-force. 

12.  Two  coils,  A  and  B,  of  fine  insulated  wire,  made  exactly 
alike,  and  of  the  same  number  of  windings  in  each,  are  placed 
upon  a  common  axis,  but  at  a  distance  of  10  inches  apart.    They 
are  placed  in  circuit  with  one  another  and  with  the  secondary  wire 
of  a  small  induction-coil  of  RuhmkotiTs  pattern,  the  connections 
being  so  arranged  that  the  currents  run  round  the  two  coils  in 
opposite  directions.     A  third  coil  of  fine  wire,  C,  has  its  two 
ends  connected  with  ft  Bell's  telephone,  to  which  the  experi- 
menter listens  while  he  places  this  third  coil  between  the  other 
two.      He  finds  that  when  C  is  exactly  midway  between  A  and 
B   no  sound  is  audible  in  the  telephone,   though  sounds  are 
heard  if  C  is  nearer  to  either  A  or  B.     Explain  the  cause  of  this. 
He  also  finds  that  if  a  bit  of  iron  wire  is  placed  in  A  silence  is 
not  obtained  in  the  telephone  until  .C  is  moved  to  a  position 
nearer  to  B  than  the  middle.     Why  is  this  ?  .  Lastly,  he  finds 
that  if  a  disc  of  brass,  copper,  or  lead,  is  interposed  between  A 
and  C,  the  position  of  silence  for  C  is  now  nearer  to  A  than  the 
middle.     How  is  this  explained  ? 


INDEX. 


443 


INDEX. 


N.B. — The  Figures  refer  to  the  Numbered  Paragraphs. 


ABSOLUTE  Electrometer,  261 
Galvanometer,  200 
Measurements,  325%.,  363,  36 1 
Units  of  Measurement,  255 

Accumulator,  47,  48,  266 

of    currents    (see    Secondary 
Batteries) 

Action  at  a  distance,  21,  56,  972 

Air  condenser,.  48,  267 

Air,  resistance  of,  291,  325^ 

Aldini,   Giovanni,   Experiments  on 
Animals,  229 

Amalgam,  electric,  41 

Amalgamating  zinc  plates,  162 

Amber,  i 

Amoeba,  the  sensitiveness  of,  230 

Am-meter,  200  (its) 

Ampere,  Andrt,  Theory  of  Electro- 
dynamics, 331,  334 
"Ampere's  Rule,    186 
Laws  of  Currents,  332 
suggests  a  Telegraph,  423 
Table  for  Experiments,  333 
Theory  of  Magnetism,  338 
Ampere,  the,  323 

Angles,  Ways  of  Reckoning,  129 
Solid,  133 

Animal  Electricity,  68,  231 

Anion,  210 

Annual  variations  of  magnet,  143 

Anode,  207 

Arc,  voltaic,  371 

Arago,  Franfois  Jean, 

classification  of  lightning,  304 
magnetisation  by  current,  326 
on  magnetic  action  of  a  voltaic 

current,  191 
on  magnetic  rotations,  401 


Armature  of  magnet,  101 

of  dynamo  •  electric    machine, 

407,  409,  410 

Armstrong,  Sir  Wm.t   his  Hydro- 
electric Machine,  44 . 
Astatic  magnetic  needles,  190 

Galvanometer,  190 

Atmospheric  Electricity,  64,  301,  306 
Attracted-disc  Electrometers,  261 
Attraction    and    repulsion    of  elec- 
trified bodies,  i,  3,    18,   20, 
66,  236 

and  repulsion  of  currents,  331, 
and  repulsion  of  magnets,  76,  80 

332 

Aurora,  the,  144,  145,  309 
Ayrton  (W.  £.)  and  Perry  (John) 
on  contact  electricity,  72 
on  dielectric  capacity,  271 
value  of  "v,"  365 
am-meter,  200  (6is) 
voltmeter,  360  (ef) 
Azimuth  Compass,  134,  136 


B.  A.  UNIT  (or  ohm),  323,  363,  364 

Back  Stroke,  26,  304 

Bain's  Chemical  Writing  Telegraph, 

218 

Balance,  Wheatstone's,  358 
Ballistic  Galvanometer,  204 
Bancalari  on  diamagnetism  of  flames, 

344 

Battery  of  Leyden  Jars,  54 
Batteries,  voltaic,  154,  167,  182 

,,      list  of,  178 
secondary,  415 

Beccaria,    Father   G-,    on    electric 
distillation,  223 


444 


INDEX. 


Beccaria,  Father  G.,  on  atmospheric 

electricity,  306 

Becguerel,  Antoine  Cesar,  on  atmo- 
spheric electricity,  307 
onAdiamagnetism,  339 
Becquerel,  Edmond,  on  photo- voltaic 

currents,  389 
BecquereL,  Henri,  on  magneto-optic 

rotation,  387 

Bell,  Alexander  Graham,  his  Tele- 
phone, 435 

The'Phptophone,  389 
Bells,  electric,  432 
Ben-net's  Doubler,  23 

Electroscope,  13,  25 
Bertsch's  Electric  Machine,  45 
Best  grouping  of  cells,  351 
Bichromate  Battery,, 165 
Bifilar  Suspension,  118,  262,  336 
Biot,  Jean  Baptiste,  Experiment  with 

hemispheres,  30 
Law  of  magnetic  distribution, 

'1,8 

on  atmospheric  electricity,  307 
Bismuth,    diamagnetic  properties  of, 

87,  313,  339 

Blasting  by  electricity,  280,  370 
Blood,  diamagnetism  of,  339 
.Boracite,  67 

"Bound"  electricity,  24,    149   {foot- 
note) 
Boltzntann,   on  Dielectric  capacity, 

270,  271,  390 
Boyle,    H#n.    Robert,    on   electrical 

attraction,  2 
Branched  circuif,  353 
Breaking  a  magnet,  106 
Breath-figures,  297 
Bridge,  WheatstpnS*,  358 
British   Association   Unit,    323,    364, 

3<5s- 

Brugntans  discovers  magnetic  repul- 
sion ,of  bismufli,  339 

Brush  discharge,  290 

Brush's  dynamo-electric  machine,  411 

Bunsen's  Battery,  173 


CABLE,  Atlantic,  274  (footnote),  275, 

296,  4>9 
submarine,  429 

,,          as    condenser,   274, 

296,  430 
Calot,   Sebastian,   on  magnetic   de- 

'clination,  136 

Cailleiet  on  resistance  of  air,  291 
Calibration  of  Galvanometer.  108 


Callan's  Battery,  172 
Cailaud" s  Battery,  176' 
Cantofi,  John,  discovers  Electrostatic 
Induction,  18  , 

on  Electric  Amalgam,  4* 
Candle,  electric,  373 
Capacity,  definition  of,  246 

measurement  of,  362 

of  accumulator  or  condenser, 
50,  267,  277 

of  conductor,  37,  47,  247,  277 

of  Ley  den  Jar,  50,  267 

specific  inductive,  21,  49,  268 
272. 

unit  of  (electrostatic),  247 

unit  of  (practical),  276 
Capillary  Electrometer,  225,  265 
Carnivorous  Plants,  sensitive  td'elec- 

tricity,  230 
Carri,  P.,  Dielectric  machine,  45 

on  magnets  of  cast  metal,  97 
Cascade  arrangement  of  Jars,  279 
Cautery  by  electricity,  369 
Cavalto    Tiberius,    his    attempt   lo 
telegraph.  423 

his  pith -ball  electroscope,  3 

on  a  fireball,  304 

on  atmosphenc  electricity,  303, 

306 

Cavendish,    Hon.    H.,   on   Specific 
Inductive  capacity,  268,  269 

on    nitric    acid    produced   by 

sparks,  286 
Ceca,  •  Father^   on  atmospheric  eTeo 

tricity,  306 
Cell,  voltaic,  152 
Charge,  electric,  7 

resides  on  surface,  27 

residual  of  Leyden  Jar,  53,  372 
Chart,  magnetic,  136,  169 
Chemical  actions  in  the  battery,  159 

laws  of.  166,  211,  417 

of  spark  discharge,  286 

outside  the  battery,  205,  412     - 
Chemical  test  for  weak  currents,  218, 

286 

Chimes,  electric,  43  _ 
Chronograph,  electric,  433 
Circuit,  152 

simple  and  compound,  181 
ClarVs  (Latimer)  standard  cell,  177 
Clausius,  R.,  theory  of  Electrolysis, 

418 

Cleavage,  electrification  by,  60 
Clocks,  electric,  433 
Cobalt,  magnetism  of,  86 
Coefficient  cf  Magnetic  induction,  89 

3T3 
of  mutual  induction,  391 


INDEX. 


445 


Coercive  force.  89 

Colour  of  spark,  289 

Columbus,  Cristo/ero,   en  magnetic 

variation,  136 
Combustion  a  source  of  electrification, 

M 

Commutator,  375,  309,  407 
Compass  (magnetic),    Mariner's,    79, 

134 

Compound  circuit,  181 
Condensation   48 
Condensers.,  48,  267 

standard.  276 

use  of,  275 

Condensing  electrorcope,  71,  149 
Conduction,  27,  158 

by  liquids,  205 

of  gases,  158 

Conductivity,  158,  346,  348- 
Conductors  and  Non-ccnductors,  8,  27 
Consequent  Poles,  104,  109 
Contact  Electricity,  71,  149 

Series  of  metals,  72 
Continuous  electrophorus,  23,  45 
Convection  of  Electricity,  45,  337 
Convection-currents,  properties  of,  337 
Convection-induction  machines,  45 
Convection-streams  at  points,  35  (a), 

43.  249 
Cooling  and  heating  of  junction  by 

current,  380 
Cost  of  power  denved  from  electricity, 

3?8 

Coulomb^  Torsion  Balance,  13,  119 
Law  of  Inverse   Squares,    16, 

117,  119,  235,  245 
on  distribution  of  charge,  35, 248 
Coulomb,  the,  32  3 
Couple,  magnetic,  123 
Crookea,    William,    on    shadows    in 

electric  discharge,  293 
on    repulsion    from    negative 

electrode,  300 
Crown  of  cups.,  1 51 
Cruickshank' s  Trough  Battery,  iCa 
Crystals,  electricity  of,  06 

dielectric  properties  of  370 
magnetism  of,  343 
Crystallisation,  61 
Cumming 's  phenomenon,  382 
Cuneii!,'  discovery  of  Leyden  Jar,  52 
Current,  efier:!.'  ilue  to,  153 
Current  Electricity.  147 

strength  of,  158,  179 

,,        unit  01,  196 

Current -re\er?er  (see  Commutator) 
Current  sneeU,  340 
Curvature  arfects  surface-density,  35, 
340 


Curves,     magnetic     (see    Magnetic 

Figures) 
Cuthberlson's  Electric  machine,  38, 

289 
Cylinder  Electrical  machine,  39 


DAILY  variations  of  magnet,  14* 
Dalibard's  lightning-rod.  302 
Daniell's  Battery,  170 
Davy's  (Marie)  Battery,  175 
Davy,  Sir  Humphrey,  magnetisation 

by  current,  326 
discovers  electric  light,  371 
electrolyses    caustic    alkalU 


hes, 


41 


De  Haldat.  magnetic  wntmg,  .11 
De  la  Rive  s  Floating  Battery,  194 
DelaRue,  Chloride  of  Silver  Battery, 
174,  291 

on  electrotyping,  420 

on  length  of  spark,  291 
Declination,  Magnetic,  136 

variations  of,  136,  141 
Decomposition  of  water,  206,  413 

of  alkalies,  417 

Deflections,  method  of,  118,  123,  3253 
Dellmann's  electrometer,  260 
Density  (surface)  of  charge,  35,  248 

magnetic,  127,  311 

Deivar,  James,  on  currents  generated 
by  light  Li  the  eye,  231- 

his  capillary  electrometer,  225 
Diagram,  thermo-electric,  383 
Diamagnetic  polarity,  342 
Diamagnetism,  87,  339 

of  flames,  344 

of  gases,  340 

Diaphragm  currents,  224 
Dielectric  capacity  (see  Specific  IK 
ductive  Capacity) 

strain,  56,  272 

strength,  284 
Dielectrics,  8,  49,  270 
Differential  Galvanometer,  203 
Dimensions  of  Units  (see  Units) 
Dip,  or  Inclination,  137 

variation  of,  .141 
Diplex  signalling,  428 
Dipping  Needle,  137 
Discharge  atfected  by  magnet,.  294 

brush,  43 

by  evaporation,  223 

by  flame,  7,  291 

conductive,  282 

convective,  43,  283 

disruptive,  381 


446 


INDEX. 


Discharge  affected  by  points,  43,  390, 

302 

effects  of,  43,  984,  986 
electrical,  7,  280 
glow,  zoo,  302  (footnote) 
Emit  of,  248 
sensitive  state  of,  294 
velocity  of,  296 
Discharger,  Discharging-tongs,  51 

Universal,  54 

Disruption  produces  electrification,  60 
Dissectable  Leyden  Jar,  55 
Dissipation  of  Charge,  299 
Distillation,  electric,  223 
Distribution  of   Electricity,   28,   35, 

348,  349 
of  Current,  240 
of  Magnetism,  104,  122 
Divided  Circuit,  353 

Touch,  93 

Dolbear*s  Telephone,  436 
Doubler,  23,  45 
Double  Touch,  94 
I>ry-Pile,  182,  264 
Huboscq  s  Lamp,  372 
"Du  Fay's  experiments,  4,  37 
Duplex  Telegraphy,  375,  428 
duration  of  Spark,  296 
Huter  on  Electric  Expansion,  273 
Dynamic    Electricity    (see    Current 

JLlectricity) 

Dynamo-electric  machines,  408 
Dyne,  the  (unit  of  force),  355 


EARTH,  the,  a  magnet,  88 
currents,  275,  403 
electrostatic  capacity  of, 
intensity  of  magnetisation,  313 
magnetic  moment  of,°32sb 
used  as  return  wire,  423 

Earth's  magnetism    (f 
Magnetism) 

Edison,  Tkomas  A  lvat  electric  lamp, 
374  ;  steam -dynamo,  411  (5X 
carbon  telephone,  436 
meter  for  currents,  216 
quadruple*  telegraphy,  438 

Edlur.d  on  galvanic  expansion,  cri 

Eel,  electric  (Gymnotus),  68   ' 

Electrics;  i 

Electric  Air-Thermometer,  288 
Cage,  34 
Candle,  573 
Clocks,  433 
Distillation,  293 
(Fiietiona!)  machines,  39 


Electric  Egg,  the,  393 
Expansion,  273 
Force,  153  (Jooincte\  341 
Fuze,  286,  370 
Images,  250 
Kite,  302 
Lamps,  373 
Light.  37* 
Mill  or  Fly,  43 
Oscillations,  295 
Osmose,  232 
Pistol,  286 
Shadows,  293 
Shock,  226 
Wind,  43 
Electricity,  theories  of,  6,  300 
Electro-capillary  phenomena,  225 
Electro-chemical  equivalents,  211,  211 
Electro-chemistry,  4x2 
Electrodes,  207 

unpolarisable,  331 
Electrodynamics,  331 
Electrodyaamometer,  336,378  (bis.) 
Electrolysis,  208 

laws  of.  211,  4x4,  417 
of  copper  sulphate,  209 
of  water,  207,  413 
theory  of,  4x4 
Electrolytes,  207,  417 
Electrolytic  ccnvection,  41} 
Elcctrcniagaets,  98,  326 

laws  of,  330 

Electromagnetic  engines  (motors),  £75 
Electromagnetics,  3x0 
Electromagnetic  theory  of  Light,  390 
Electromagnetism,  326 
Electrometallurgy,  419 
Electrometer,  absolute,  261 
attractcd-disc,  261 
capillary,  225,  265 
Delltnann's,  260 
divided-ring,  71 
Peltier's,  260,  307 
portable,  261 
quadrant  (Sir  W*  T 

362 

repulsion,  260 
torsion,  15 
trap-door,  261 
Elcctromctive-force,  155 
measurement  of,  360 
unit  of,  322,  323 
Electromotors,  375 
Electro-Optics,  383 
Electrophorus,  22 

continuous,  23,  45 
Electroplating,  421 
Electroscopes,  n 

Bohnenbtrgsr1 1,  13,  064 


INDEX. 


447 


Electroscopes,  Benntfs  gold-leaf,  13, 

Fechneifs,  ^64 

Gaugain's  discharging,  259 

Gilberts  straw-needle,  12 

Hankel's,  264 

Henley's  quadrant,  14 

Pith-ball,  2,  3 

Volttfs  condensing,  71,  149 
Electrostatics,  7,  233 
Electrotyping,  420 
Energy  of  charge  of  Leyden  Jar,  270 

of  electric  current,  378 
Equator/  Magnetic,  78 
Equipotential  surfaces,  242,  310  (f) 

magnetic,  310 

Equivalents,  electro-chemical,  212 
Erg,  the  (unit  of  work),  255 
Evaporation  produces  electrification, 

*-63l  3°3  u 
discharge  by,  323 

Everett,  James  £>.,  on  atmospheric 

electricity,  307 

on    exact   reading  of   galvan- 
ometer, 202  (footnote) 
on  intensity  of  magnetisation 

^  of  earth,  313 

Expansion,  electric,  273,  386 
Extra-current  (self-induced),  404 


FAILURE  and  exhaustion  of  batteries, 

1 60 

Fall  of  Potential  along  a  wire,  263,  357 
Farad,  the  (unit  of  capacity),  276,  323 
Faraday,  Michael,  molecular  theory 

of  electricity,  6 
chemical  theory  of  cell,  i56 
dark  discharge,  290 
Diamagnetism,  339,  340,  344 
discovered  inductive  capacity, 

21,  269,  271 

Discovery  of  magneto  •  induc- 
.  tion,  391 

Electro-magnetic  rotation,  375 
experiment  on  dielectric  polar- 
isation, 272 

gauze-bag  experiment,  31 
nollow-cube  experiment,  31 
ire-pail  experiment,  34 
laws  cf  electrolysis,  211,  214 
Magnetic  lines-of-force,  108, 402 
on  A  rago's  rotations,  401 
on  dissipation  of  charge,  291 
on  identity  of  different  kinds  of 

electricity,  217,  218,  286 
Voltameter,  214 


Faraday.   Michael,    Magneto -optic 

discovery,  387 
predicted  retardation  in  cables, 

274 
Faure's  Secondary  Battery,  415 

Favre's  experiments  on  Heat  of  Cur- 
rents, 368 

Feckner's  electroscope,  264 
Feddersen,    W.,  on  electric   oscilla- 
tions, 296 

Ferromagnetic  substances,  339 
Field,  magnetic,  105,  191,  312 
Figures,  magnetic  (see  Magnetic 

figures) 
electric,  297 

Fire  of  St.  Elmo,  302  {footnote) 
Flame,  currents  of,  291 

diamagnctism  of,  344 
discharge  by,  7,  291 
produces  electrification,  62 
Fleming's  Battery,  182 
Fontana  on  electric  expansion,  273 
Force,   electric,   155   (footnote),  241, 
251,  252 
magnetic,    83,   155  (footnote), 

328 

electromotive,  155 
Foucault's  Regulator  Lamp,  372 

Interrupter,  398       „ 
Franklin,      Benjamin,      discovered 
action  of    points,  mentioned 
in,  35  (c),  43.  3™ 
cascade  arrangement  of  Leyden 

Jars,  279  _ 
Electric  Chimes,  43 
Electric  Kite,  302 
Electric  portraits,  288 
his  charged  pane  of  glass,  47 
invents  Lightning  Conductors, 

3°S 
kills  turkey  by  electric  shock, 

256 
One-fluid  theory  of  Electricity, 

•  ,0 

on  seat  of  charge,  55 
theory  of  the  Aurora,  309 
"  Free  "  electricity,  24,  149  (footnote) 
Friction  produces  electrification,  i,  10 
Frog's  legs,  contractions  of,  148,  * 
Froment  s  Electromotor,  375 
Fuze,  electric,  286,  370 


Gaivani,  Aloysius,  observed  move- 
ments of  frog's  leg,  148 


44* 


INDEX. 


Galvant,  Aloystus,  on  preparation  of 
frog's  limbs,  229 

on  Animal  Electricity,  231 
Galvanic     Batteries     (see      Voltaic 
Batteries) 

Electricity  (see  Current  Elec- 
tricity) 

Taste.  237 

Galvanism  (see  Current  Electricity) 
Galvanometer,  107 

absolute,  «oo 

astatic,  198,  331 

ballistic,  204 

constant  of,  200 

differential,  203 

f>n  Bin  Reytnond't,  331 

tfelmJtoltt's,  IQO 

reflecting  (Sir  W.  Thomson's). 
or  mirror,  aoa 

sine,  201 

tangent,  199 

Galvanoplastic  (see  Electrolysing) 
Gal  \anoscope,  188 
Gas  Battery,  416 
Gases,  resistance  of,  158 
Gassiot,  /.  P  ,  on  stric=,  294,  300 
Contain,  Jean  Mothte,  discharging 
electroscope,  259 

on  Pyroelectricity,  66 

Tangent  Galvanometer,  199 
G.fitss,  F.,  invented  absolute  measure- 
ment, 32sa 

magnetic    moment    of    earth, 


magnetic  observations,  313 
Gay,   Lussac,   on  atmosphenc  elec- 

tricity, 307 
Geissler's  tubes,  291 
Geniez  on  electric  distillation,  223 
Gil-son    and    Barclay    on    dielectric 

capacity  of  paraffin,  270 
Gilbert,     Dr.     William,     discovers 

electrics,  i 
discovered   magnetic  reaction, 

83 
discovers   that   the  earth   is  a 

magnet,  88,  135 
heat  destroys  magnetism,  09 
his     balanced  -  needle    electro- 

scope, 12 

observation  of  moisture,  9 
observations  on  magnets,  78 
on    de  -  electrifying    power    of 

flame,  291 

on  magnetic  figures,  108 
on  magnetic  substances,  85 
on  magnetic  permeability,  84 
on  methods  of  magnetisation, 

«6,  97 


Gilding  by  Electricity,  431 
Globular  lightning,  304 
Glow  Discharge,  290,  302  (footnote] 
Glowing  of  wires.  369 
Gold-leaf  Electroscope  (see  Electro- 
scope) 
Gordon,  J.  £.  H.,  on  magneto-optic 

rotatory  power,  387 
on  dielectric  capacitj,  270,  271 
on  length  of  spark,  291 
Gramme's  dynamo-electric  machine, 

410 

Gravitation  Battery,  176 
Gray,  Stephen,  discovers  conduction, 

on  lightning,  302 
Grotthuss'  theory,  160,  418 
Grove,    Sir    William   R.,    his  ,Gai 

Battery,  416 
Grove's  Battery^  171 
magnetic  experiment,  113 
on  electric  property  of  Flame, 

291 

Guard-ring,  Guard-plate,  248,  261 
Guericke,  Otto  von,  discovered  elee 

trie  repulsion,  3 
invents  electric  machine,  38 
observes  electric  sparks,  9 
Gunpowder  fired  by  electricity,  286, 

288,  370 
Gymnotus  (electric  eel),  68,  318 


Halts  phenomenon,  337 

Hankers  electroscope,  264 

Harris,     Sir    tr'.    Snow,    his    unit 

Leydenjar,  259 
attracted  •  disc      electrometer, 

261 

on  length  of  spark,  291 
Heat,  effect  of,  on  magnets,  99,  too 
,,  batteries,  183 

„  conductivity,  349 

Heating  effects  of  currents,  171,  366, 

380 

due  to  magnetisation,  113,  401 
effect  of  sparks,  a88 

,,     dielectric  stress,  3-73 
local,  at  electrodes,  41' 
Helmholtz,     Hermann     L.  on 

effect  of  current  on  s%     .  2?1 
Electrolytic  convection,  418 
Equations   of    Self  •  induction, 
-,f>5 

Galvanometer,  199 

Henry,       Joseph,        invented        tii* 
"sounder,"  423 


INDEX. 


449 


Henry,  Joseph^  on  induced  currents  of 

higher  orders,  406 
Holt*t  W,,  his  electric  machine.  46 

on  electric  shadows,  393  (,  foot- 
note] 

on  tubes  having  unilateral  re- 
sistance, 300 

Hofkinson,  John,  on  dielectric   cap- 
acity of  glass,  970 
on    residual     charge    and     its 

return,  53,  872 
Horizontal  component  of  magnetism, 

123,  138 
Hughes,  David  Edward,  the  Print-. 

ing  Telegraph,  423 
the  Microphone,  437 
Humboldt,  Alexander  von,  on  elec- 
tric eels,  68 

discovers  galvanic  smell,  228 
produced  electric   contractions 

in  fishes,  229 
Hunter,     Dr.    John,    on    effect    of 

current  on  sight,  228 
Hydroelectric  machine,  44 


IMAGES,  electric,  950 
Incandescent  electric  lights,  374 
Inclination  (or  Dip),  137 

variation  of,  141 
Index  Notation,  3250 
Induced  charges  of  electricity,  18 

currents,  391 

Induction  (electrostatic)  of  charges, 
if 

(ma.S~netic\  Hnes  of,  89 

(magnetic)  of  magnetism,   89, 

3*3 

„          coefficient  of,  342 
(magneto-electric)  of  currents, 

39» 

Induction-coil  or  Inductorium,  398 
Induction-convection  machines,  45 
Ind  ictive-capacity,  specific,  21,  49, 

»oS.   272 

Insulators,  8,  27 
intensity  of  current,  179 

of  earth's  magnetic  force,  138, 

3s  5a 

Oi  magnetic  field,  312 
of  magnetisation,  313 
Inverse  Squares,  Law  of,  16,  117,  235, 

*45 

Inversion,  Thermo-electric,  382 
Ions,  210 

Isoclinic  lines,  139 
Isogomc  lines,  139 


JacoU,  Merits  Hermann,  on  local 
action,  162 

discovers  galvanoplastic  pro- 
cess, 4:0 

his  boat  propelled  by  electricity, 

theory  of  electromotors,  377 
Jablochko_ff,  Paul,  his  battery,  182 

electric  candle,  373 
Jar,  Ley  den,  51 

v       capacity  of,  50,  267,  277 
„       cascade  arrangement  of, 

279 

,,       discharge  of,  51,  295 
„       discovery  of,  53 
,,       energy  of  charge  of,  278 
„       seat  of  charge  of,  55 
„       spark  of,  289,  296 
„       theory  of,  267 
Unit,  259 

Jenkin,  Fleemingt  on  cable  as  con- 
denser, 274 

on  retardation  in  cables,  296 
Joule,  James  Prescott,  on  effects  of 

magnetisation.  113 
Law  of  Heat  of  Current,  367 
Mechanical  equivalent  of  Heat, 

255.  414 

ou  atmospheric  electricity,  306 
on    lifting  •  power    of    electro- 
magnet, 326 
/ow//-effect,  the,  380,  367 


KATHODE,  207 
Kation,  210 
Keeper,  101 

Kerr,   Dr.  John,  Electro  •  optic  dis- 
coveries, 273,  386 
Magneto-optic  discoveries,  IIA, 

388 

Kinntrsley,   Elijah,    Electric   Ther- 
mometer, 288 
Kinhho/.  Gustav,  Laws  of  Branched 

Circuits,  353 
Kite,  the  electric,  302 
Kohlrausch,  F.,  on  residual  charge, 

272 

on  electro-chemical  equivalent, 
an  (footnote) 


LAMELLAR  magnetisation,  107 


INDEX. 


Laminated  magnets,  95 

Law  of  Inverse  squares,  16,  117,  335, 

»45 

Leakage,  rate  of,  299 
LectencM't  Batteryt  173 
Le     Bailiff  on     diamagnetism     of 

antimony,  339 
Lemonnicr    discovers     atmospheric 

electricity,  306 
Length  of  spark,  391 
Lettifs  Law,  396 

alcohol  calorimeter,  367 
Leyden  Tar  (see  Jar) 
Licktenoerjf  t  figures,  297 
Lifting-power  of  magnets,  103 

of  electromagnets,  328 
Light  affects  resistance,  389 
•  Electric,  371 
Electromagnetic  theory  of,  365, 

polarised,  rotated  by  magnet, 

.  "4.  387,  388 
Lightning,  9,  302,  304 

conductors,  32,  305 

duration  of,  296,  304 
Lines-of-force,  electric,  243 

due  to  currents,  191,  329,  334 

magnetic,  89,  108,  310,  312 
Lifpmann,    G.,    Capillary    Electro- 
meter, 225,  265 
Liquids  as  conductors,  205 

'resistance  of,  348 
"  Local  Action  "  in  batteries,  161 
Lodestone,  76,  340 
"  Long-coil     instruments,  353 
Loss  of  Charge,  15,  299 
Louis  XV.  electrifies  700  monks,  226 
Lullin's  experiment,  285 
Luminous  effects  of  spark,  289,  400 

M 

MACHINE,  Alternate-current,  411 

Electric,  38 

Compound-wound,  411 

convection-induction,  45 

cylinder,  39 

dynamo-electric,  408 

Holttts,  46 

hydro-electrical,  44 

invention  of,  38 

magneto-electric,  407 

plate,  44 

Winter's,  40 

Magne-crystallic  action,  343 
Magnet,  breaking  a,  106 
Magnets,  natural  and  artificial,   76, 

77,  326 

Magnetic  actions  of  current,  184,  318, 
396,  339,  334 


Magnetic  attraction  and  repulsion,  Co, 

xxo 

cage,  84 
curves,  108,  191 
field,  105,  191,  312,  327 
figures,  xo8,  109,  no,  191 

,,       theory  of,  126 
fluids,  alleged,  qx 
force,  83,  310  (e) 

.,      measurement     of,     118 


•  3a 

mdt 


iuction,  89 

„        coefficient  of,  342 
iron  ore,  76 
lines-of- force,  89,  108,  109,  xxo, 

316 
lines-of-force  of  current,   191, 

320,  329 
maps,  139 
meridian,  136 
metals,  86,  339 
moment,    123   (/ootnot«\   313, 

Sff 

needle,  79,  134 

oxide  of  iron,  76,  172  (_footx:*s} 

paradox,  a,  128 

pole,  unit,  125 

potential,  310,  314,  •*  13 

proof-plane,  402 

saturation,  102,  330 

„  Beetz,  on,  115 

screen,  84 

shell,  107,  XQ2,  311  (K) 
„  >  force  due  to,  137 
„  '  potential  due  ip,  127,  3-- 

storms,  145,  309 

substances,  85,  339 

units,  321 

writing,  xxx 

Magnetisation,  coefficient  of  (or  sus- 
ceptibility), 89,  313 
intensity  of,  313 
lamellar,  107 

mechanical  effects  of,  1x3 
methods  of,  92-98,  327 
solenoidal,  107 
sound  of,  113,  434 
time  needed  for,  330 

Magnetism,  76 

action  of,  on  light,  114,  387 
caused  by  heat,  98 
destruction  of,  99 
distribution  of.  104 
of  gases,  339,  387 
lamellar,  107 
laws  of,  Si,  116,  310,  330 
permanent,  90,  3x3 
residual,  102 


INDEX. 


451 


Magnetism,  solenoidal,  107,  314 

temporary,  90,  102,  313 

terrestrial.  88,  135 

theories  of,  91,  115,  338 

unit  of,  125 
Magnetite,  76 
Magneto-electricity,  74,  391 
Magneto-electric  induction,  391 

machines,  407 
Magnetographs,  146 
Magnetometer.  124 

self-registering,  146 
Magneto-optic  Rotations,  387 
Magnets,  artificial,  77 

compound,  95 

forms  of,  101 

lamellar,  iy/ 

laminated,  95 

methods  of  making,  92  98 

natural,  76,  101 

power  of,  103 
Mance's  method,  361 
Maps,  magnetic,  139 
Mariner's  Compass,  134 
Marked  pole,  80 

Mascart,    J£.t    on    self  •  registering 
apparatus,  288 

on  atmospheric  electricity,  308 
Mattewci.   Catlo,   on   physiological 
effects,  68,  230 

on      electromotive  -  force1     in 

muscle,  231 
Maynooth     Battery    (see     Callans 

Battery) 

Maxu  U,    fames    Clerk,     Electro- 
magnetic theory    of   Light, 

337.  365.  390 
on  Electric  Images,  250 
on  protection  from  Lightning, 

32,  3<>5 

on  residual  charge  of  jar.  272 
on  self-repulsion  of  circuit,  334 
rule  for  action  of  current  on 

magnet,  193,  317 
Theorem    of  equivalent  Mag- 
netic shell,  192,  318 
Theory  of  Magnetism,  115 
Measurements,  electrical,  355-363 

magnetic,  118,  3253. 
Mechanical  effects  of  Discharge,  284, 

43 
etects  of  magnetisation,  113 

,,       in  dielectric,  272 
Medical  Applications  of  Electricity, 

232,  369 
Megohm,  323 
Meidinger's  Battery,  176. 
Meridian.  Magnetic.  136 
Metallo-chromv,  432 


Microfarad  condenser,  276 
Microphone,  the,  437 
Milli-ampere,  323 

M  imosa.  the,  electric  behaviour  of,  230 
Minolta's  Battery,  176 
Mirror  Galvanometer,  203 
Moisture,*  effect  of,  i,  8,  2cp 
Molecular  theory  of  Electric  action,  6 

actions  of  current,  221 
Moment  of  Couple,  123 

of  inertia,  32  $a 

magnetic,  123  (Jbotnoie),  3253 
Morse  Telegraph  instrument,  425 
Mouse-mill  (sea  Repfenisher) 
Mailer,   Johannes,    on    strength   of 

electromagnets,  330 
Multiplier,  Sthweigger' s,  18g 
Muscular  contractions,  229,  231 
Musschenbroek,     Peter     van,     dis- 
covery of  Ley  den  Jar,  52 

on  Magnetic  Figures,  no 
Mutual  Induction,  coefficient  of,  320, 

397 
Mutual  Potential,  coefficient  of,  320 


N 

Napoleon  IIJ.'s  Battery,  182 
Needle,  magnetic,  79 
Needle  Telegraph,  424 
Negative  electrification,  4,  300 
Newton,  Sir  Isaac,  observations  on 

action  and  reaction,  83 
bis  lodeslone,  103 
suggests  electric  origin  of  light- 
ning, 9,  302 
suggests     glass    for     electric 

machines,  38 
Niaudefs  Battery,  173 
Nobili,  Leopoldo,  on  muscular  con- 
tractions, 68 
on  currents  of  animal  electricity, 

231 

discovers  N chili's  rings,  422 
Non-conductors,  8 
Non-electrics,  2 
North  and  south,  81,  135 
North  magnetic  pole,  the,  81,  135 
Null  methods,  263 


Oerstedt,  Hans  Christian,  discovers 
magnetic  action  of  current,  184, 
185,  191 

Ohm,  Dr.  G.  S.,  179 

"  Ohm's  Law,"  160,  345 


452 


INDEX. 


Ohm,  the,  or  unit  of  resistance,  333 

,,  determination 'of,  364 
One-fluid  theory  of  electricity,  6 
Optical  strain,  electrostatic,  386 

,,      electromagnetic,  387 
Oscillations,  electric,  295 

method  of -(for  electrostatics), 

120  (footnote),  235 
method  of  (for  magnetic  mea- 
surement), 120, 121, 122,  32$a 
Osmose,  electric,  222 
Other  sources  of  electricity  than  fric- 
tion, 10,  57 
Ozone,  ao8,  298,  302  (footnote) 


Page,  Charles  G.t  discovers  magnetic 

sounds,  113 

Parallel  currents,  laws  of,  333 
Paramagnetic,  339 

"  Passive"  state  of  iron,  172  (footnote} 
Peltier,  Athanase,  his  electrometer, 

«6p,  307 

heating  effect  at  junctions,  380 
theory  of  thunderstorms,  303 
Penetrative,  power  of  discharge,  284   , 
Periodicity  of  aurora   and  magnetic 

storms,  144,  145,  309 
Perry  aad  Ayrton  (see  Ayrton  and 

Pitt,  Voltaic,  150      . 
Pith-ball  electroscope,  2,  3 
Phosphorescence  caused  by  discharge, 

292 
Photo -voltaic  property  of  selenium, 

S»9 

Photophbne,  389 
Physiological  actions,  226,  287 
Plane,  the  proof-,  29  / 

,,  for  magnetism,  402 

Plant/,  Gaston,  his  secondary  bat- 
teries, 4^      .  ^ 
on  globular  lightning,  304 
Plants,  electricity  of,  69,  230 
Plate  condenser,  48,  268,  277 
electrical  machine,  40 
Plucker,  Julius,  on  masne-crystallic 

action,  343" 

Po^gendorff,J.  C.,  his  battery,  165 
Points,  density  of  charge  on,  35,  249 

discharge  at,  39,  42,  43,  249 
Polarity,  diamagnetic,  343 

magnetic,  82,  106,  1x5 
Polarisation  (electrolytic)  in  battery 

cells,  163,  414 

of  Voltameter,  973,  413,  415 
remedies  for,  165  , 


Polarised  ligh*  rotated  by  magnetic 

forces,  387 
relay,  428 
Poles  of  magnets,  7_8,  122 

of  pyroelectric  crystals,  66 
of  Voltaic  battery,  154 
Porrefs  phenomenon,  222 
Portable  electrometer,  261 
Portative  force,  103 
Positive  and  negative  electrification 

4'  30? 
Potential,  electric,  37,  237 

„         zero,  37/-2S9 
magnetic,  310,  314,  315 

„        due  to  current,  318 
mutual,  of  two  circuits,  319, 

320 

Pouillet,  Claude  S.  M.,  sine  galvan- 
ometer, 201 

tangent  galvanometer,  199 
Power,  transmission  of,  376 
Practical  Units,  323 
Preece,    William  Henry,  on  space 

protected  from  lightning,  305 
Pressure  produces  electrification,  65 
Priestley,  Joseph,  on  electric  expan- 
sion, 273 

Prime  condtlctor,  39 
Printing  telegraphs,  423 
Proof-plane,  20 

„  o    (magnetic),  402 
Poisson    on    magnetism  in  crystals 

343 

Protoplasm,  electric  property  of,  331 
Pyroelectricity,  66 


Quadrant     electrometer     (Sir    W. 

Thomson's),  262 
electroscope  (Henley's),  14 
Quadruplex  telegraphy,  428 
"Quantity"    arrangement    of    cells, 
1    etc.,  181  • 

of  electricity,  unit  of,  \j,  236 
Quetelet,   E.,   on  atmospheric   elec- 
tricity, 308 
Quincke,  Georg,  on  diaphragm  cur- 

.  rents,  224     , 
on  electric  expansion.  273 
on   electro  -  optic    phenomena, 
386 


Ray,  electric  (torpedo),  68 
Recovery,  elastic,  27* 


INDEX. 


453 


Redistribution  of  charge,  36 
Reflecting  galvanometer,  202 
Registering  magnetographs  and  elec- 
trometers, 146,  307 
Reis,  Philip,  invention  of  telephone, 

434 

Relation  between  currents  and  mag- 
nets, 184,  318,  326,  391 
between  current  and  energy, 

between  current  and  heat  and 

light,  366 
Relays,  426 

Replenisher,  45,  261,  262 
Repulsion  and  attraction  of  electrified 
'bodies,  i,  3,  18,  20,  66,  236 
and  attraction,  experiments  on, 

and  attraction  of  currents,  331 
and  attraction  of  magnets,  76, 

80 

Repulsion  electrometers,  260 
Residual  charge  of  Leyden  jar,  53,  272 
„       of  cable,  274,  430 
„      of  Voltameter,   272, 

magnetism,  102 
Resinous  electricity,  4 
Resistance,  27,  158,  179,  346 

absolute  unit  of,  363,  364 
affected  by  temperature,  349 
„          light,  389 
,,          sound,  436 
as  a  velocity,  363 
bridge  or  balance,  358 
coils,  359 
internal,  of  cell,  181,  350 

,,        „  measurement 

of,  361 
law's  of,  347' 
measurement  of,  356 
of  gases,  158,  348 
of  liquids,  158,  349 
specific,  348 
Retardation     of    currents     through 

cables,  274,  296,  430 
Retentivity  (magnetic),  90,  313 
Return  shock  or  stroke,  26,  304 
Reyntond,  Du  Bois,  his  galvanometer, 

231 

on  animal  electricity,  231 
unpolarisable  electrodes,  231 
Rheocord,  356 
Rheostat,  356 
Rheometer,   \ 

Rheoscope,    >  see  footnote  to  197 
Rheotrope,     ) 

Riess,  Peter,  on  electric  distribution, 
35 


Riess,  Peter,  on  length  of  spark,  291 
electric  thermometer,  288  (foot- 
note). 

Ritchie's  electromotor,  375 
Rittcr,  Johann  IVilhelm,  on  action 

of  current  on  sight,  228 
his  secondary  pile,  415 
on  subjective  galvanic  sounds, 

230 
on  the  sensitive  plant  (Mimosa), 

230 

Rolling  friction,  10 
Romagnosi,  Dr.,  discovers  magnetic 

action  of  current,  18^ 
Romas,  De,  his  electric  kite,  302 
Ronalds,   Sir  Francis,   invented    a 

telegraph,  423 
Rotations,  electromagnetic,  335 

AragJs,  401 

Rowland,  Henry  A .,  on  magnetic 
effect  of  electric  convection,  337 
on  intensity  of  magnetisation, 

3*3 

Ruhmkorff's  induction  coil,  398 
commutator,  399 
electromagnet,  339 


S 


St.  Elmo's  fire,  502  (footnote) 
Salts,  electrolysis  of,  417 
Sanderson,  J    Bnrdon,   on  electric 

sensitiveness  of  carnivorous  plants, 

231 

Sawdust  battery,  158,  176 
Sckiveigger 's  multiplier,  189 
Secondary  batteries,  178,  415 
Secular  variations  of  magnetic  ele- 
ments, 141 
SeebecKs   discovery  of  thermo-elec- 

tricity,  379 
Selenium,  photo-voltaic  properties  of, 

389 

Self-induction  of  circuit,  404 
Self-recording  apparatus,  146,  288,  307 
Self-repulsion  of  current,  334 
Sensitive  plant,  behaviour  of,  230 
Series,  union  of  cells  in,  171 
Shadows,  electric,  293 
Sheet  conductor,  flow  of  electricity 

in,  354 

Shell,  magnetic  (see  Magnetic  Shell) 
Shock,  electric,  226 

of  current,  226 

"Short-coil"  instruments,  352 
Shunt,  202,  353 
Siemens,  Carl  Wilhelmt  -on  heating 

effect  in  Leyden  jar,  373 


454 


INDEX. 


Siemens,  Carl  Wilkslxi,  his  dynaiuo- 

electric  machine,  409 
hit  longitudinal  armature,  407 
Sight  affected  by  current,  228 
Silurui,  the,  68 
Sine  galvanometer,  201 
Single  touch,  93 
Single-fluid  cells,  169 
Siphon-recorder,  431 
Sinee's  Battery,  165,  169 
Soap-bubble,  electrified,  3 
Solenoid,  329 

magnet,  314 
Solid  angles,  133 
Solidification,  61 
S^und  of  magnetisation,  113 
Sounder,  the,  425 
Sources  of  electricity,  10,  57 
Spark,  9,  43,  281 

duration  of,  296 
length  of,  44,  291,  302 
Specific  resistance,  348 

inductive  cajscity,  21,  49,  268, 

272 

Speed  of  signalling,  274,  273,  296,  430 
Sphere,  distribution   of  charge   ever 

35(«),  248,  249 

Spotiizivoode,  William,  on  stnae,  254 
Siffitia.rtt    Balfojur,    on    atmospheric 

electricity,  308 
on  magnetic  storms,  144 
Storms,  magnetic,  14; 
Standards  of  resistance   (see  Resist- 
ance Coils) 
Strain,  dielectric,  56 
Strength  of  current,  158,  179 

„  in  magnetic  mea- 

sure, 195,  156 

Strergth  of  magnet  pole,  102 
of  magnetic  shell,  315 
Striae  in  vacuum  tubes,  292,  294 
Sturgeon)    W.,   invents   the   electro- 
magnet, 326 

Submarine  telegraphs,  429 
Sulser's  experiment,  227 
Symmer,  on  two  kinds  of  electrifica- 
tion, 4 

Surface-density  of  charge,  35,  248 
limit  of,  248 
of  magnetism,  127,  311 
Swamme retain' s  frog  experiment,  229 
Swatt'i  electric  lamp,  374 


T 


Tait,  Peter  Gut  Arse,  electrification 
by  evaporation  of  sulphate  of  copper 
solution,  63 


Tait%  Peter  Gvikrie,  thermo-electric 

diagram,  383 

Tar  ^ent  galvanometer,  109 

Taste  affected  by  current,  227 

Telegraph,  electric,  423 

Bain's  chemical,  218 
Morse's  instrument,  425 
needle  instrument,  424 

Telegraphy,  diplex,  428 
duplex,  428 
quadruplex,  428 
submarine,  429 

Telephone,  Philip  Kei/t,  434 
currents  ot  229 
Dolbear's,  436 
Ediscn's  (carbon),  438 
Gralutm  Bell's  (articulating^ 

435 

Varleyfs  (condenser),  272 
Temperature  affects  resistance,  183 

affected  by  resistance,  369 
Tension   of   electrostatic  forces,    248 

(footnote) 

Terqitem,     A.,    parrot-cage    experi- 
ment, 31 

Terrestrial  Magnetism,  88,  135 
Test  for  weak  currents  (chemica1),  218, 

286    . 

for  weak  currents  (physiologi- 
cal), 229 

Testing  for  faults,  427 
Tetanisation  produced  by  interrupted 

currents,  230 
Theories  of  Electricity,  6,   300,  aad 

preface,  be. 
Theories  of  Magnetism,  91,  115 

„       At/lire's,  338 
„       Max-well's,  115 
Theory  of  Electrolysis,  Joule's,  414 

GroltMtss's  and  Clavstus's,  418 
Thermo-electric  currents,  ) 
Thermo-electricity,  f  ?°'  379 

Thermo-electric  Diagram,  383 
Thermo-electromotive  Series,  382 
Thermo-pile,  384 

Thompson,  Sih'anus  Phillipt,  on 
magnetic  figures  due  to  cur 
rents,  33^ 

on  Magnetic  writing,  nz 
on  Nobilt's  rings,  422 
on     Positive    'and     Negative 
^states,  300 
on  opacity  of  Tourmaline,  390 

(  footnote) ' 
Thomson,    Joseph.   /.,     on     Contact 

Electricity,  73  ;  value  of  "  v,"  305 

Thomson,    Sir    William,    the    Re- 

plenisher  (or  Mouse- Mill),  45,  a6t. 

S02 


INDEX. 


455 


Thomson,   Sir    William,    Proof   of 

Contact  Electricity,  71 
Attracted  •  disc  Electrometers, 

261 

Divided-ring  Electrometer.  71 
Electric    convection    of    Heat 
(the  "  Thomson-effect "),  383 
Mirror  Galvanometer,  202,  431 
Modified  Daniel Ts  Battery,  176 
on  atmospheric  electricity,  306 
on  Electric  Images,  250 
on  length  of  spark,  291 
on    nomenclature    of    Magnet 

Poles,  81  (footnote) 
on  sounds  in  condensers,  272 
predicts    electric    oscillations 

295  (footnote) 

Quadrant  Electrometer,  262 
Siphon  Recorder,  431 
Thermo-electric  Diagram,  383 
Water-dropping  Collector,  307 
Thunder,  9,  304 
Thunderstorms,  302 

Theory  of,  303 
Tinfoil  Condensers,  47,  275 
Tongs,  Discharging-,  51 
Torpedo  (electric  fish),  68,  218 
Torp^doe^,  fuzes  for  firing,  zao,  370 
Torsion  affected  by  magnetisation,  1 1  _, 
Torsion  Balance,  or      )     (Coulomb's) 
Torsion  Electrometer   )         15,  119 
Total  action  of  magnet,  3253 
Tourmaline,  66,  297,  390  (footnote) 
Transformers,  400  [376 

Transmission  of  P^wer  by  Electricity 
Tubes  of  force,  243,  311 
Two-fluid  cells,  170 
Two-fluid  theory,  6 
Two  kinds  of  Electrification,  4,  5 
,,     Magnetic  poles,  Si 
TynJall,  John,  on  diamagnetic  polar- 
ity. 34* 
on  magne-crystallic  action,  343 


UNIT  Jar,  259 

Unit  (Electrostatic)  of  Electricity,  17, 

236 

(Electrostatic)  of  Capacity,  247 
Magnetic  Pole,  125 
of  difference  of  potential,   242 

322,  323 

of  Electromotive-force,  322^  323 
of  Resistance,  322,  323 
of  Strength   of    Current,    196, 
3".  3*3 


Units,    Fundamental    and    Derived. 

254.  255 

dimensions  of,  258,  324 
Electrical  (Electrostatic),  857 
Electromagnetic.  322,  333 
Magnetic,  321 
Physical   Dimensions  of,    258, 

„  324>.  35,1 
Practical,  323 

Universal  Discharger,  54 

Urtt  Dr.,  on  Animal  Electricity,  229 


"  »,"  values  of,  365,  390 

Vacuum,      induction       takes      place 

through,  50,  84,  89 
partial,  spark  in,  9,  292 
spark    will    not   pass   through, 

291 

Vacuum-tubes,  292 
"  Variation,"  the  (see  Declination) 
Variation   of  Declination    and    Dip, 
secular,  141  ;  annual,  143  ;  diurnal, 
14?  ;  geographical,  136 
Varley,  C.  A.,  his  Telephone,  273 
Vegetables.  Electricity  of,  oo 

carnivorous,    sensitiveness    of, 

230 
Velocity  of  Discharge,  206 

of  Electricity  (alleged),  296 
of  Light,  365,  300 
Verdetjs  Constant,  387 
Vibration  produces  Electrification,  59 
Vitreous  electricity,  4 
Volt,  the,  323 
Volta,Alessandro,  his  Electrophorus, 

33 

Condensing    Electroscope,   71, 

149 

Contact  Series,  72 
Crown  of  Cups,  151 
on  Atmospheric  Electricity,  307 
on  Contact  Electricity,  71,  148 
on  Electric  Expansion,  273 
on  Electrification  due  to  com- 
bustion, 62 
Subjective     Sounds     due     to 

Current.  228 

Volta's  Law,  72,  148,  156 
Voltaic  Pile,  150 

Voltaic  Electricity  (see  Current  Elec- 
tricity) 
Arc,  371 

Battery,  154,  167;  Pile,  130 
Cell,  simple,  152 
Voltameter,  214,  215,  316 
Voltmeter,  360  (ef) 


456 


INDEX. 


WATER,  Electrolysis  of,  206,  413 
Weber,  the  323 

Wtber,   IVilhelni,.  the   Electro-dyna- 
mometer, 356 

on  diamagnetic  polarity,  342 
Wheatstone,    Sir   Charles,    on    the 

brush  discharge,  290 
Automatic  Telegraph,  423 
Dynamo -electric  Machines,  408 
on  supposed   velocity  of  elec- 
tricity, 296 

WheatstonJs  Bridge  or  Bal- 
ance, 358 

WiedciHann,    Gusfav,   on   effect    of 
magnetism  on  torsion,  113 


Wiedemann,    Gnstav,    on    diaraag- 

netism  of  platinum,  339 
Wilde,  Henry,  Electric  Candle,  373 
Magneto-electric  Machine,  <oj 
Wind,  Electric,  43 
WShJer's  Cell,  182 
Wollastoiis  Battery,  169 
WiiUner  on  dielectric  capacity,  270 


Z 


Zant&onCt  Dry  Pile,  13,  182,  264 
Zanotti,  experiment  on  grasshoppe 

229 
Zero  Potential,  37,  139 


THE    END, 


A    000  037  201     1 


